In classic strategy games such as Total Annihilation and in Supreme Commander the player not only had their usual units but also had a commander -- a very powerful central unit that was particularly lethal and capable of doing many different things.
Demigod, in many respects, is the logical progression of this game mechanic. In Demigod, players choose a hero to be their Demigod in a quest to becoming increasingly powerful.
In individual games that take place in arenas that, in my opinion, are a strategy gamer's panacea (even classic maps like Painted Desert in TA can't hold a candle to some of the cool arenas in Demigod), the Demigod will rise in level as he (or she) gains experience allowing for increasingly powerful abilities.
What is also cool is that outside these individual skirmishes these Demigods grow in power. This has some very important ramifications. Besides making the single player experience much more interesting, it introduces a much better on-line experience.
Let me put it like this: Demigod is aiming to solve some of the most basic problems in on-line gaming: Because your Demigod gets better in a persistent universe, experienced players have an incentive to keep with their hero and its stats rather than "smurfing".
Moreover, it creates a great deal of interesting match-making possibilities. Why not allow the option of someone who is really good at the game with a high level Demigod face off against 3 or 4 opponents online? In Total Annihilation, I regularly would play against 4 or 5 players versus me and that was on a "level" playing field. Of course, players can still opt to the traditional on-line skirmishes where everything starts on the same playing field. But with Demigod, players will have more options.
I am sure I'm not the only guy who remembers the beginning of Fellowship of the Ring (the movie) where Sauron is trashing Elven and human butt and thinking "ooh, I'd so like to be able to do that!" In Demigod you are the Sauron.