So I get it all but this: when Booker was killed by Elizabeth, what did that achieve and what did that little bit after the credits with Booker going into Anna/Elizabeth's room mean? Did they both die completely, in every universe, or did it start fresh with Booker and Anna/Elizabeth together at the beginning with no such complications?
It is revealed that the game takes place in a multiuniverse. Booker is also Zachary Comstock (The Prophet) in multiple parallel universes, meaning that Comstock and Booker are the same person who have been brought together by means of an interdimensional passage. The difference in name comes from a deciding point in his life where he could have gotten a baptism and be reborn under a different name (which would have been Zachary Comstock). Booker, in this new reality with his other self, sees what a horrible person Comstock is and all the hell Elizabeth is put through and decides to end him, which through Elizabeth's powers means he could kill Comstock before is he was born and save Elizabeth from all this trouble. He does not realise until later that killing Comstock would do this to himself. After realizing it, he goes back to this original deciding point in time where he could be been 'reborn' through baptism. In the ending, Elizabeth takes Booker on a journey to an infinite number of lighthouses, all representing the "beginning" of some kind of journey that is always the same with slight variations. After Booker realizes that he is just a pawn in an infinite number of similar sequences, he decides to allow Elizabeth kill him during his baptism so that he can save his daughter.