Singleplayer is where you play against different AI tribes, selected randomly, only chosen if unlocked (save the Luxidoor easter egg). There are currently two different singleplayer modes: Perfection and Domination. Singleplayer is one of two ways to play, the other being the Pass and Play Multiplayer. Side Note: Online Multiplayer has been in beta testing, but still needs work.
In perfection mode, your objective is to obtain the highest score possible in 30 turns. There are different strategies for this on the strategies page. During these 30 turns, you can choose whether you want to fight enemy tribes, build an economic superpower, or both. If your score is high enough it is posted on the global high score. Some determined players have climbed their way to 100k, double what is needed for three stars. This mode offers a little more freedom than Domination. You can play this mode in 4 difficulties, Easy, Normal, Hard, and Crazy, each affecting the score differently. Perfection's rough equivalent in Pass and Play (Multiplayer) is "Glory".
In domination mode, your objective is to defeat all other tribes in as little turns as possible. Your rating in domination is calculated based on the turns you took, the units you lost, the tribes you defeated, and the difficulty. You can square off against other tribes in 4 difficulties, Easy, Normal, Hard, or Crazy, each affecting the overall score differently. You can also have up to 10 opponents to have. If you achieve 100% in a Domination game with a certain tribe, that tribe will gain white streaks going from the center outwards to represent your accomplishments. Domination's rough equivalent in Pass and Play (Multiplayer) is "Might".