Attack Points (AP) are gained from attacking other players and barbarians, in particular from killing units and structures.
Defense Points (DP) are gained from killing attacking units at your own city or while defending somewhere else.
Simply the total amount of Loot a player has looted.
Your Influence Points (IP) are determined by the total number of levels of all your buildings combined in one city. This number also determines when you can create a new city. See Influence Points for more details.