Culture was introduced to the Civilization series first in Civ 3. It is produced by certain buildings: Temple, Cathedral, Colosseum, Library, University, Research Lab, and the Palace.
All Wonders also produce culture.
Culture represents the impact of your civilization's customs, arts, and philosophy on the people in the countryside surrounding your cities, and is represented in the game by borders.
City Cultural Value and Borders
All Wonders of the World and many city improvements generate culture points every turn. These accumulate over time and when the total culture value of a city reaches certain thresholds (10, 100, 1,000, 10,000, 20,000, etc.), a border expansion is triggered. Pay attention to the culture box on the City Display to judge when expansions will occur. The amount of culture each Wonder or improvement contributes doubles after 1000 years.
Civilization Culture Value
The sum of the cultural values of all of your cities is your civilization's cultural value. It comes into play when you conquer an enemy city (and resistance is determined), conduct diplomacy with a rival, or when you and a rival both have a legitimate claim on a terrain square. In all cases, if your civilization is more valuable culturally than your rival, that's good -- and the greater the discrepancy between you, the better.
There are five global cultures in the game: Amerindian, Greco-Roman, European, Far Eastern, and Middle Eastern. Global culture determines the look of cities and citizens, and nations of the same global culture tend to start near each other and are more tolerant in diplomacy.