Why was this a bad move?

25. Qb3 (by Black). The moves shown in the analysis say that I can win a rook for a knight, but I don't understand why. Why not defend the d6 square, or move the rook/king? Was the Black queen in danger?

The c6-h1 diagonal is a vulnerable spot for white, with the broken pawn structure and the king sitting on h1.  I wouldn't pay too much attention to the specific move list in the analysis, just visually take in that the diagonal has power - the queen is doing something there.  By contrast, the queen does  essentially nothing on b3 after nc4 or bc3.  

25. Ne3 Qb3 26. Nc4! (threatening fork) Rd8 27. Bc3! (with idea of a4 followed by Ra4 & capturing Queen) 

If Qa5 the Nxe5! with a powerful attack on black's king 

Thus, Black gives up the Exchange to prevent King hunt & Potential Queen Capture.