A "god game" is a game in which you portray a deity, whether the only one, or one of many, and in which you control or otherwise influence worshipers. The game which gave birth to the genre was Peter Molyneux's classic Populous, from Bullfrog games. Molyneux is the most prolific creator of god games, with several sequels to Populus (including a 3D version) and more recently, the highly successful Black & White (soon to be followed by Black & White 2).
Most god games are top-down representations, to represent a god's-eye view. Some of them include other aspects, such as the side-scrolling platformer modes in Actraiser in which you control an avatar in order to defeat assorted bad guys who are troubling your followers.
For comparison, examine turn-based strategy games like Civilization, in which you play the part of an extremely long-lived leader of a people, and realtime strategy games like Warcraft, in which you play a sort of implied god role by directly controlling your units from above.