Bioshock: Infinite starts in medias res. There are a lot of details of the "hows" and "whys" that will be explained as you play.
From the outset, you should know that the player character is Booker DeWitt, a private detective who has been hired by a pair of rather unusual people to retrieve a rather unusual girl from a rather unusual city.
The game is quite linear, so there's little to no chance that you'll get lost and not be able to figure out what to do next. Just keep following along, and eventually the plot will start to come into focus.
However, the plot can be relatively difficult to understand, so I won't go so far as to say that eventually things will make sense :)
There is little to no dependency between Bioshock 1/2 and Infinite. If you haven't played the first two, you might miss out on some understanding of a few late game moments, but it's nothing major. I believe the "Burial at Sea" DLC is more tightly tied to Bioshock 1, so you might want to play that game first if you plan on playing the DLC.