There are basically three different game modes:
1) Normal games between humans and/or AI's. These are your typical "skirmish" or "custom game" games in other RTS games. There are two teams - each team ranging from 1 to 5 players - that play against each other on a single arena.
2) There is also the online Pantheon tournament. In this mode, you choose a side (dark or light) and can choose any of the 4 Demigods on that side. You play with others on your side against players of the opposite side, and the results are added to an overall total. Many different people play many different games until either Light or Dark has reached the goal number of points.
3) In singleplayer, there is a "tournament" mode. You choose one of the eight Demigods and play 8 different 4v4 matches with random teammates. At the end of each match, the favor points that you earned are added to an overall total. At the end of the 8 matches, the Demigod with the most favor points wins.