Zones of Control, abbreviated as ZOC, is a game concept which prevents you moving freely in zones controlled (or partially controlled) by enemy forces.
Zones of control are only enforceable on some terrain, only on land tiles. When ZOC applies, the general rule is that a unit which is adjacent to an enemy occupied tile cannot move directly to another tile which is also adjacent to an enemy occupied tile. An enemy occupied tile is one with a foreign unit of a type that imposes ZOC, unless you have an Alliance pact with that nation. Adjacency means any of the eight tiles surrounding a unit for rectangular grids, or six tiles for hexagonal grids.
In the following special cases, units can move regardless of ZOC:
A unit moving directly into or out of a city.
A unit moving onto a tile already occupied by a friendly unit.
A unit moving to or from a terrain where ZOC cannot be enforced; for instance, a land unit disembarking from a boat which is on an ocean tile.
A unit type which explicitly ignores ZOC, such as Diplomats and Spies.
Notes:
ZOC does not restrict unit attacks, only movement.
Units may only impose ZOC when they are on terrain that supports it. Thus, units that are not native to terrain effectively cannot impose ZOC except for the special case where they are in a city.
An enemy city counts as an enemy occupied tile if there are any units inside the city, but not if the city is empty.
TIP: You can infiltrate enemy zones by first moving in a Diplomat (or some other unit which ignores ZOC), and then moving regular units onto the tile now occupied by the Diplomat. By repeating this process (and optionally leaving some units behind to keep tiles occupied), you can make a path through enemy territory.