A Great General provides a 50% bonus to combat to anybody in the square he occupies. The square he occupies is the square the unit is pinned to. You can receive a Great General by defeating a unit with power equal or greater than your unit or by a gallant "attack" or "defense."
There is a glitch involving the Great General in the Nintendo DS version of the game. If the unit with the Great General disembarks a naval unit in a certain way, the general will occupy a different square than the unit and travel beside it. If an enemy attacks the general, your general will send out another general without the lower part of its sprite.