A nation's territory is comprised of all the land and water tiles it currently controls directly or indirectly. In a very real sense, the land you control is your nation, because it includes its physical representation in the world. A leader may imagine that he or she has power over great expanses (sometimes they may even accuse you of settling into lands they consider their own!), but in reality the leader only controls limited parts of the game map.
For convenience, different civilizations' territories are associated with a different, fixed color. For example, the territory of the English civilization is red, while the territory of the American civilization is dark blue. On the main map, territorial borders are visible through a thick line in the relevant color which passes along the tiles it controls; on the mini-map territories are even clearer, as the entire territory of different nations is colored.
As a first, and maybe not-that-obvious effect, all tiles within your territory and all neighboring tiles are fully visible at all times. After all, your empire's subjects and agents move constantly through your land and report what they see.
Territory and Cities
All territory in the game is controlled by cities, thanks to their civilizing influences on the nomadic tribes that otherwise claim the land. As mentioned above, the nation's leader may have all the delusions of grandeur he wishes, but it is the real, cultural influence of his cities that determine the actual number of tiles under his direct control. This is best visualized during city capturing, when the entire territory this city controls switches nations, along with the city itself. In the normal course of events, the more cities you have, the greater territory you control. However, this may not always be the case, as sometimes cities producing lots of Culture can expand a nation's territory much faster and farther than others that produce little or no Culture. Nevertheless, every time a new city is founded, all unclaimed tiles immediately adjacent to it are added to that nation's territory, and they will remain there, even if the city produces 0 Culture.
If a city is destroyed (razed, or hit with a Nuclear Missile when it has less than 6 Population), all territory it controls becomes unclaimed (neutral) again, as civilization steps back and the wilderness reigns supreme again. This is also the only case when tiles which previously belonged to a civilization will become neutral again, instead of simply switching to another civilization.
Each city is able to further expand the territory it (and thus your nation) controls. This depends on how much Culture the city produces. The maximum size of a city is 11 tiles in diameter. For the specific mechanics of border expansion, look below.
Territory and Movement
National territories are considered inviolate; this also includes the territories of City-States. Under normal circumstances units from civilizations or City-States cannot enter the territories of other nations. They can enter territories of City-States, but if they are not at least Friends with the City-State in question, they will incur an Influence penalty with it. When a nation signs an Open Borders treaty with another nation (that is, when the other nation allows Open borders), its units may now enter the other nation's territory freely. While in it, they will also be able to use its Roads and Railroads.
Workers and other civilian units may enter City-States' territory without repercussions. However, they still cannot enter other nations' territory. The only exception to this rule is for Missionaries and Great Prophets - they are able to enter other nation's territory at all times. However, the Missionary suffers "damage" when doing this!
These rules may restrict movement considerably, especially in the early game (when several tiles belonging to another nation close off whole sections of the map, and you don't have the tech to go around), and in the late game, when (almost) all land is controlled by one nation or another.
Note that you can enter any territory when you are at war with its owner. Since Barbarians are always at war with everybody, they may move freely everywhere!
Territory and Economy
You may only economically use land (and water) which is inside your territory. Citizens from cities may only work on tiles that are inside your territory and within a 3-tile radius of the city they inhabit. Most tile improvements can only be constructed inside your territory (with small exceptions); from this follows that access to any resources is only possible if they are in your territory! Note that to make strategic use of strategic and luxury resources you will need to construct an improvement on their tile, but it doesn't need to be within 3 tiles of a city. It is still recommended, however, to have a city closer so that you can use the entire potential of the tile.
Having certain Natural Wonders within your borders will net your empire a permanent boost in Happiness (which is separate from the boost you get for finding them). However, you will lose this bonus if you lose control of the territory that contains the Wonder.
Territory and Units
Military procurement is accomplished much faster and more efficient inside your own land. Thus, land units heal twice as fast when inside your territory; sea units may heal only when inside your territory. Note that for healing purposes the territory of another nation or City-State which are friendly (that is, you have Open Borders treaty with them), is considered home territory. Also, units may only upgrade to next-era units when inside your territory - in this case, the territory of other civilizations and city-states doesn't qualify as your own, even if they're your allies!
Territory and War
Finally, many special abilities in the game (such as the Shoshone civilization's unique ability) confer combat bonuses for all units when fighting within their own territory. The Great Wall wonder activates a special effect which hinders movement for all hostile units entering that nation's territory. This effect, however, expires for nations that discover Dynamite.
It is possible to attack hostile units when they are inside the territory of a nation you're not at war with, and with which you have no Open Borders. But you can do this only with ranged units, since melee units need to actually enter the tile the other unit is in, which is impossible without an Open Borders treaty.
Any city which produces Culture will further expand the territory of your nation. The process occupies one tile at a time, thus enlarging the empire. Note that you can only expand into unclaimed (neutral) tiles, not into other civilizations' or city-states' territory.
The process of border growth is automatic (that is, you have no control of it), but it is not random - more important tiles are occupied first. The target tiles selected by the engine depend on the presence of these factors, in order of importance:
- Luxury resources
- Strategic resources
- Bonus resources
- Tiles bordering one of the above
If no such features are present nearby, the next tiles marked for occupation become the ones closest to the city. For example, if in one direction it has expanded three tiles away, in another two, and in all others it is only occupying the nearby tile, the city would try to expand two tiles away in all other directions. In such cases, or whenever there are two tiles of equal interest according to the list above, the engine marks all applicable tiles and, whenever the turn comes, makes a random selection.
The rate of natural border expansion for each city depends on how much Culture it produces per turn, and on how many tiles it has already acquired. For each successive tile there is a required amount of Culture that needs to accumulate; that amount grows for each successive tile, and is subject to empire bonuses and other modifiers. Note that one-time Culture gifts (such as the ones gained by exploring Ancient Ruins), temporary bonuses (such as the double cultural growth the empire gains after finishing first for the World's Fair Project), or other general cultural bonuses (such as Culture gifted by City-States) do not contribute towards border expansion! They only apply to the general pool accumulating for Social Policies and Ideological tenets' purchases.
Borders can also be expanded by using Gold to purchase tiles adjacent to the current border, but only in the workable city area (3 tiles away in every direction).
A city's borders will only expand within a 5-tile radius (not including the city tile itself). While a city cannot work the "extra" tiles (i.e. those outside the 3-tile radius), a civilization is still eligible for strategic and luxury resources located there (if they have been improved).
Only tiles that don't belong to anyone may be occupied via Culture! However, there is a way to take over tiles belonging to other nation: using the Great Artist's ability Culture Bomb, which will take over all surrounding tiles, regardless of whom they belong to! (In Gods & Kings, this ability was transferred to the Great General, when he builds a Citadel.) Be wary, though - this will surely have diplomatic repercussions!
A city's boundaries can extend over water, blocking navigation by units of other civilizations without an Open Borders agreement, but not trade routes. A city built on an isthmus that is only one tile wide will act as a canal, but only for the civilization that owns it and only for naval vessels and Work Boats. Embarked units cannot pass through; they must land and re-embark. Other civilizations' warships can only pass through with an Open Borders agreement, although they still can't end their turn in the city. But again, sea trade routes may pass through that canal without an agreement.
In certain cases (primarily when you settle new cities, or dig up Artifacts), your actions near, or inside another nation's territory may cause a diplomatic uproar. Know that all leaders are conscious about their own borders, and what they consider "their" territory. This last means the land that a certain leader intends to expand into, and which is fairly close to his or her current borders. They won't take it well if you settle a city right there. They also won't take it well if your borders consistently expand right next to theirs.
When you work on an Antiquity Site which is inside another nation's territory, and you decide to extract an Artifact from it, the other nation will complain - after all, you are stealing their historical relics! On the other hand, if you decide to turn the site into a Landmark, they will be thankful. The same is valid for a City-State - you will gain Influence points with it if you convert a site into a Landmark. You won't lose Influence, though, if you extract an Artifact.
It is important, though not essential, for your nation to control as much territory as possible. One of the items increasing your Victory score is exactly Land, which means the number of tiles you control. However, as we know, Victory points are not essential for winning the game (unless you reach the maximum number of turns). It is true that sometimes the quality of the land you control is more important than the quantity. A small empire controlling lush lands with lots of resources will do better than a huge empire controlling desert or tundra.
That being said, the odds are that the more land you control around the Industrial Era, the bigger the chances that, as you progress technologically, the new strategic resources you uncover will happen to be already inside your territory.