Warning: BioShock Infinite spoilers ahead!
So, the end of BioShock Infinite is confusing. It does a reveal, then another, then another, and it feels like half of the ending sequence is spent explaining the other half. And the explations that aren't right at the end are packed into the easy-to-miss audiologs scattered around the world. For those of you who are still baffled, here is my explanation:
What? You haven't completed BioShock Infinite yet? Go away! Why did you click this link? This game puts a lot of its emotional payload inside of big reveals, so spoilers really matter. Anyway. Final warning.
So the good guy is also the bad guy? And the woman you saved is also the child you lost? And the scientist who created the problem also devised the solution? And the only way to stop the bad guy is to kill yourself? What does it all mean, and what is the game trying to say? The best way to unravel this is by going over the plot in chronological order instead of the order it's revealed to us in the game.
The events begin with the massacre at Wounded Knee. Booker DeWitt - accused by his compatriots of having "teepees in his family tree" - wanted to prove himself as loyal, so he became even more savage than his fellow soldiers. He burned women and children alive in their tents and killed as many people as he could. After the war, these deeds haunted him. He sought comfort in religion. And here we have our big split.
The most important thing to note here is that the world of BioShock Infinite uses the many-worlds interpretation where everything that can happen, does happen, along one of the endless branches of an ever-splitting set of possible realities. (This is a real theory, and it was popularized by theoretical physicist Bryce DeWitt.)
In one universe, Booker backs out of baptism at the last second. He figures he doesn't deserve to be forgiven, and the crimes he's perpetrated can't be washed away with water. He walks away from religion and instead distracts himself from his past with booze and gambling. He ends up with a woman, gets her pregnant, and she dies in childbirth. This leaves Booker alone, with heaps of gambling debts, and little baby Anna to raise by himself.
In the other universe, Booker accepts his baptism. When he emerges from the water he renames himself Comstock. The process seems to give him new purpose in life. He becomes a preacher and builds a congregation. He seems to have a twisted view of both baptism and his religion. Instead of repenting of his evil, he acts like baptism is some kind of "get out of guilt for free card." Instead of feeling remorse at his crimes, he celebrates them and uses them to build his persona as a heroic figure.
He teams up with Dr. Lutece. He provides the funding for her science, and she provides the dimensional tears that allow Comstock to peer into the future. With this tool, Comstock is able to make himself into a prophet. His cult grows, his wealth grows, he marries Lady Comstock, and eventually he founds the flying city of Columbia.
At some point Comstock gets the idea to baptize the world in fire. Baptism worked so well for him, so he figures it will be good for the human race in a "doomsday that kills all unbelievers" kind of way. Unfortunately for his scheme, peering through the tears has aged Comstock. He's not going to live long enough to see it through. He needs an heir. However, his time-peeking has also sterilized him.
With the help of Lutece, he jumps to one of these side-universes to buy baby Anna from the alcoholic loser Booker. This arrangement would naturally appeal to both men. Comstock would like the idea because the little girl would still be "his" in a genetic sense. Booker would like the idea because he'd be solving his gambling debts and giving his little girl a proper home with a family that wants her.
Booker backs out of the agreement at the last minute. He tries to rescue his kid from the hands of Comstock just as Comstock is slipping back into his own universe. They struggle over the kid and the tear slams shut on baby Anna's finger, leaving a tiny part of her in Booker's universe while the rest of her is living in Comstock's.
Comstock renames the child Elizabeth and sticks her in a tower. Having her body split between universes has given her the ability to open not just tears back to her own universe, but to any universe she likes. Dr. Lutece comes up with the siphon, which will deaden Elizabeth's powers and prevent her from escaping.
The sudden appearance of a new baby upsets Lady Comstock. She figures her husband is just cheating on her and threatens to tell everyone. Comstock has her killed.
Not much happens while the girl is growing up. About the only notable thing is that Dr. Lutece opens a tear and pulls through a different version of herself from another universe. This Dr. Lutece is a man. She calls him her "brother" and things are kind of weird for a bit but everyone gets used to the idea.