Its a common move in this position. Black will often sacrifice on c3, opening the c-file. Whites move gets the king off of the open file, and protects the a-pawn.
Why this move?

What Bacon said is mostly correct, however black does have immediate concrete threats with Bd7, Qa5, and b4, when the a2-pawn might drop off.
If you look at grandmaster games where one side castles queenside, you will find that Kb1 (or Kb8) is played the vast majority of the time, You could think on this move as "completing" castling, getting the king off an open diagonal, and protecting the rook pawn.
If the rook lines up on c8 later(which it usually does) then the rook will be lined up with the king, making pawn thrusts more dangerous. Kb1 in advance prevents that.
It's interesting the way opening lines become very popular and then just seem to fade away. This position was a matter of some theoretical interest at one time, but it seems to have disappeared from grandmaster play around 20 years ago! I could only find one grandmaster game after 2008. In GM games, 14.Kb1 was the most frequent choice by a pretty big margin.
Trying to, but can't figure out why KB1 is the favorite move here. The engine success this and it is what was played in this game. Can someone please help me understand? Am I missing an obvious defensive move? Is it making space for the bishop to come back or for the rook to take over the C1 square?
Thanks!