Why can the white king not take the queen here?
A king can only capture unprotected pieces. In this case, the Black queen is protected by the black-squared bishop.
If a king moves into a square where an enemy piece (the bishop) can recapture him, he is "moving into check," which he can't do. If a player can't move out of check with his king, either by moving away, capturing the checking piece or "interposing" (which doesn't work when the checking piece is adjacent) he loses the game.
But here, the king can move out of check by going to c3. Put the Black knight on b5 or d5, and White is check mated.