Stars are supposed to give you better command abilities.
Therefore, the more stars your general has, the better commander he is.
I'm sure it's more useful in auto-resolve but a general with a lot of stars apparently gives his men more morale and his men will obey his orders more readily.
That's what I can gather at least. I do know a 10-star AI general is pretty much unbeatable on auto-resolve so you should always try and fight out your battles with an enemy of that calibre.
"We must fight so well, that each man believes himself to be the chief cause of our victory."