You gain battle points for killing enemy units in game, either as an attacker or a defender. The amount of battle points that you get is determined by the amount of population that you kill. For example, each LS takes 10 population to build, if you were to attack 10 LS with your own LS and kill them all you would gain 100 attacking battle points.
You also get battle points for killing enemy troops that are attacking your own, albeit the way the battle points are distributed is very different. When attacking you get battle points for everything you kill, however as a defender you may only receive a certain % of the battle points if there are other units defending your city. The formula for this isn't publicly released, therefore I'm unable to give you any figures as an example. Please note that this isn't the case when defending Ghost cities, you do not receive any battle points for this.
As a final example, if you have 100 Biremes in your harbor, that belong to you, and your enemy rather foolishly decided to send 100 unescorted transport ships at you, you will get all of the defensive battle points from the attack which would be 700 defensive battle points.
If you don't understand any of this or would like battle points explained in greater detail, please let me know. Best of luck in game.
Edit: Please note that you don't get any battle points for killing the enemies militia.