In Grepolis, there are five gods, Zeus, Poseidon, Hera, Athena and Hades, with Artemis being available only in Hero Worlds. Each god can enact four different divine powers (which affect different things such as troop attack or resource income or even defence) and call upon two unique mythical units.
In the Temple you can select which god you would like to worship. Each city can choose which god to worship, however each city can only worship one god at a time. The higher the level of your Temple, the more favour you earn from your chosen god. You can spend this favour to enact divine powers or call upon mythical units.
What god is right for your city depends on your situation. It is therefore quite useful to change the god you worship many times throughout the game, as well as having different gods for each city. Do this wisely, for when you switch gods you lose all your favour as well as mythical units and divine powers from your previous god.
Divine Powers may only be cast upon certain things. Eg. a divine power that affects troops must be cast upon a troop movement.