Here are spoilers, taken straight from /v/.
The explanation is complicated as shit.
First of all, the premise:
Booker - a gambling addict who is approached to save a girl - Elizabeth from the flying city of Columbia in exchange of having his previous debt wiped clean.
On the flying city of Columbia, Zachary Comstock is regarded as a savior and a prophet.
Okay, so basically, there is a multiverse. Booker is also Zachary Comstock(The Prophet) in multiple parallel universes
Comstock and Booker are the same people who have been brought together in through some 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, not realizing until a little later that doing this to Comstock would do this to himself and after realizing it he goes back to this original deciding point in time where he could be been 'reborn' and decides to die there so his daughter doesn't have to go through what he put her through here and every dimension he became Comstock.
In the ending, Elizabeth reveals herself to be a time lord and 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. For some reason she's never told him this, even though if she had in the beginning, the whole adventure wouldn't have been necessary at all. After Booker realizes that he is just a pawn in an infinite number of similiar sequences, he decides to allow Elizabeth kill him so that he can save his daughter so that he will never live in the first place, thus also ending the life of his daughter who would have never been born, the very daughter that he was trying to save.
Then for some reason Comstock ends up being Booker, and this is a result of Booker declining or accepting a Baptism at some point in time. Booker once again allows Comstock, or rather Booker, baptize himself for some reason, thus creating another Comstock (the person he is trying to kill). Earlier (or later), Comstock buys his own daughter from himself which he sells to himself. Then a bunch of time clones show up (apparently all at the time time, did they get an invite or something?). Elizabeth(s) then start to drown Booker, who is also Comstock, without his permission, but Comstock (or rather Booker) doesn't fight it, allowing himself to die and end the cycle, instead of seeking some other more rational method of doing so.
All the events of Bioshock Infininte, BioShock 1, and Bioshock 2 are cancelled out completely, the time loop having now never existed.
Link to ending