According to Frogbeastegg's guide:

Ill starred omens
Your generals and captains will collect command stars as they win battles. These stars make them more effective. I shall quote CA developer Jerome Grasdyke on how stars work:
“It currently affects both morale and combat ability - we tried it for a while with just morale, but it ended up being not enough of a bonus. The combat calculations have changed so much from Rome to Medieval as to be unrecognisable, so it's no longer easy to equate stars to experience.

As a rule of thumb it's one point of attack per command rank, up to a maximum of 10, and this can become negative for very bad generals. Experience is one point of attack and one point of defence per chevron, plus a morale bonus.

The general's command also controls his radius-of-effect, which is set to 30 m + 5 m * command + 2 m * influence. This is used to award morale bonuses only, and is calculated between the actual general's position and the centre-point of nearby units.”