Can someone explain this computer suggestion to me? [FEN ""]

1. d4 d5 2. c4 dxc4 3. Nf3 e5 4. Nxe5 c5 5. d5 f6 6. Nxc4 b5 7. Nca3 c4 8. Nxb5 Qa5+ 9. N1c3 Bb4 10. Nd4 Bxc3+ 11. Bd2 Bxd2+ 12. Qxd2 Qxd5 13. Rc1 Nh6 14. b3 Nf5 15. bxc4 Qxd4 16. Qxd4 Nxd4 17. g3 Bb7 18. Rg1 O-O 19. e3 Nf3+


In this game, I tried to play the Catalan opening as white, but black didn't go along with it.  Early on I took free pawns (if you think this was mistake, please let me know).

Anyways, the move in question is 11. Bd2.  The computer suggests 11. bxc3, but if I do that, can’t black play Qc3+ and then take my rook?  Or would Bd2 be the appropriate response to Qc3+? It all went down hill for me after this, so I am thinking that I need to learn about this pivotal point.
Well, you were winning handily, and up material, and position. The move Nd4?? blundered a piece, and Bd2 actually makes it clearly worse, which is why the computer liked bxc3. Given two clear choices (that is, not two 0.00 or equivalent), the computer will always pick the one with the higher evaluation, and it did. Here is why it evaluated it as such.

The idea of Qd2, allowing Qxa1 is common because the queen is so out of play. Often, white has a pawn on d4, and there is no pawn on c4 for black, so Nb3 would trap the queen immediately in some similar positions.

The line after Qd2 is a tactical mess, which had it been reached by normal means (one side not losing material early), it probably could fill at least a chapter in a book. I will give a couple of lines, but there were SO many more along the way. There may be improvements for black along the way, but at the very least, despite being up a whole rook, it is actually much more dangerous for black with threats to both the king and queen.

Again, in short, the computer saw a way of keeping the black queen out of the game, and thus, it liked that line better because white may actually be significantly better in all lines, but it is hard to prove. Black is hanging by a thread. The other way was just a really bad game after Bxd2 Qxd2 Qxd2, so the choice to the computer was easy.

It is also worth noting that the black pieces, like the rooks a8 and h8 were also out-of play, and black was behind in development.

 [FEN ""]

 1. d4 d5 2. c4 dxc4 3. Nf3 e5 $4 4. Nxe5 $16 c5 5. d5 f6 6. Nxc4 $18 b5 7. Nca3 c4 $4 8. Nxb5 Qa5+ 9. N1c3 Bb4 10. Nd4 $4 {Losing a piece.} (10. a3 {Your chance to force the Bb4 to make a decision.} Qxb5 (10... Bxc3+ 11. Nxc3 $18) (10... Bc5 11. Bf4 $18) 11. axb4 Qxb4 12. Ra4) 10... Bxc3+ 11. Bd2 (11. bxc3 $1 Qxc3+ 12. Qd2 $1 Qxa1 13. g3 {This is just a better way to give back some of the material. It is very deep, but it almost wins the queen, but in saving it, the king comes under a strong attack because it is stuck in the center.} Nd7 {I will play the best computer moves here...others are worse.} (13... c3 14. Qc2 Na6 15. Nb3 $18) 14. Bg2 Rb8 15. O-O Ne7 (15... Qb1 16. Qe3+ $18) 16. d6 Ng6 17. Be4 Nc5 {The only move along with Rb1.} (17... Rb1 18. Ne6 Nb6 19. Nxg7+ Kf7 20. Qh6 f5 21. Bxb1 Qxg7 22. Qxg7+ Kxg7 23. Bb2+ Kf7 24. Bxh8 Nxh8 $16) 18. Bd5 Bd7 19. Qe3+ Kf8 20. Ba3 Rb1 21. Rxb1 Qxb1+ 22. Kg2 Ne5 23. Bxc5 g5 {Only move.} 24. h4 h6 25. Ne6+ Bxe6 26. Bxe6 Kg7 27. Bb4 $3 Qxb4 (27... Ra8 28. a3 a5 29. Bd5 Rf8 30. Qa7+ Nf7 31. Bxa5 $18) 28. Qxa7+ {Mating.}) 11... Bxd2+ 12. Qxd2 Qxd5 (12... Qxd2+ $1 13. Kxd2 f5 $1 {And Nf6 is strong.}) 13. Rc1 (13. e4 $3 {This almost impossible-to-find move was the ONLY move here, but black retains some advantage.} Qd6 (13... Qxe4+ 14. Be2 $1 {And the h1-a8 diagonal is going to win material for white, or compromise the black king position.} Nc6 {Only move.} (14... Qxg2 $4 15. Bf3 $18) 15. Nxc6 Qxc6 16. Bh5+ g6 17. Bf3 Qe6+ 18. Kd1 $16 {With the dual threats of Re1 and Bxa8.}) 14. Bxc4 Ne7 15. Rc1 Bd7 $15)