God games are a sub-genre of sims that put the player in the position of a planet or universe-ruling deity (or deities, for that matter) and then lets the player craft the virtual world using in-game mechanics that could include everything from directing the evolution of creatures towards intelligent life, building structures to honor you (the creator god), or even take on other religions in holy war.
Titles that are good examples of this genre include the older game Populous and the more recent game Black and White. Other titles that could be included in this genre are games like Spore, Godus, and the classic SNES title ActRaiser. God games can combine elements of city building sims like Simcity with mechanics taken from role-playing games and even real-time strategy titles.
Each title has its own take on what the god can influence in the in-game world but most of them revolve around building a cult following and expanding it gradually.
ActRaiser, for example, sees you raise up a tribal village to a bustling Greco-Roman temple-filled city.
You do this by encouraging worship, answering prayers, and even unleashing natural disasters to guide the development of your people.
ActRaiser is one of the few games in which god also plays urban development baron as you have to use lightning and other natural disasters to clear out old structures to make way for newer, better structures. Similarly, in Black and White, your followers have to mobilize and fight against other nearby cults until yours reigns supreme.
The gray space between these mechanics provides a lot of the amalgamation seen in god games where players can build cities, direct progress, or even destroy the world if they want to do that.