I'm not really going to go into detail on why I love this game so much because what I would say had been said by pretty much every other game reviewer. I also haven't played it since I beat it the day after it's release and that was a while ago so I don't really feel the need to go into detail. I will say though that Bioshock: Infinite had the greatest story I have experienced from a videogame in a long time and I don't think I have felt for the characters so much as I did with this game.
There are a lot of explanations out there about the ending so if you're confused the ending or even if you're not I suggest reading THIS. I feel that it is the best explanation and I agree with it most.