A unit is something that can be built in one of your cities and can move over tiles. Most are military, but the term includes peaceful people and equipment such as explorers and caravans. In general there are land, air and sea-based units. The basic mechanics have been the same for all the games up until Civilization V.
In Civ5, only one military unit is allowed to occupy a tile at a time. The limit applies to non-military units as well, but a military unit and a civilian unit may both occupy the same tile at the same time.
Call to Power has a limit of 9 units per tile (including cities).
Generally each unit can move and/or attack on each turn. Each type of unit has a basic number of movement points per turn, which may be used up in the first step or attack. Terrain and the presence of rivers, roads or railroads may affect the number of movement points used. In the original Civilization, there is some randomness in the ability of a unit to move if it has only a fraction (e.g. two-thirds) of a movement point left, and sometimes a unit will be unable to enter a mountain square on a given turn even if it has not moved in that turn.
Land units must move only onto land tiles (or onto ships except in Civilization V), sea units only onto sea tiles, but where a block of four tiles has two of each arranged alternately (i.e. opposite) any unit may cross the common corner even if it shows as an isthmus. Air units may use any tiles, and if allowed to pause at the end of one turn outside a city or carrier or airbase they may be over water.
Civilization III introduced the concept of bombardment, i.e. ranged attack, attack from a distance. In the original Civilization and Civilization II no such concept existed, but it appeared in Civilization: Call to Power.
C-evo uses the term differently: air and naval units are not allowed to enter an unguarded city but may attack it and reduce its population one point per hit unless it has City Walls.
In most games, units have defined defensive strength and defined attack strength. In the original Civilization, for example, several units have a defensive strength of 1, with the phalanx 2 and the musketeers 3, and mechanized infantry the strongest at 6, while attack strengths start at 1 and go up to 10 for land units, 12 for bombers, and 18 for battleships.
Various factors such as veteran status, city walls, and terrain can increase the effective strengths for a particular engagement, while from Civilization II onwards a unit's amount of damage may reduce its strength.
In the original Civilization no nation may build more than about 125 units. The precise number may depend on the program's accuracy in counting units, where the F2 function often shows a different number from what the player can find on the map.