An Epoch is a unit of time. In Empire Earth, it is a state when a player has access to certain units, buildings, and technology. There are 14 epochs in Empire Earth, starting from the Prehistoric Age and extending to the Nano Age. The Art of Conquest expansion adds a 15th epoch, the Space Age.
Going from one epoch to the next in game requires the player to make two buildings and also accumulate a certain amount of resources, depending on the game variant and the starting age. After advancing an epoch, you can upgrade certain units to better, more advanced units.