What does Black attack? White’s rook, which is protected by its queen. The queen can't be captured, but maybe it can be attacked and thus driven or drawn away from its defense of the rook. The only piece Black has available for the purpose is his own queen, so he lays his plans carefully. First he sees that Qb6 would also check White’s king. Again, that’s important; it means White will be forced to play QxQ, rather than just moving his queen to a square like d5 where it is safe and still protects his rook. Second, Black sees that on b6 his queen would have protection from his bishop—protection necessary when attacking an enemy queen. The fact that the guard is a bishop also is significant, because it means that if White plays QxQ, Black can recapture BxQ with check—and thus may again be able to take advantage of the priority of check. The sequence becomes clear: 1. …Qb6+; 2. QxQ, BxQ+; 3. K moves, RxR, and Black has won a rook.
The distinctive feature of this case, of course, is that the check was given not as a side effect of the capture RxR, but rather as a side effect of taking White’s queen. The principle still is the same. In this position as in the previous ones, after your opponent plays QxQ you suddenly are confronted with two captures you would like to make: a recapture of his queen, and the original capture you were hoping to make after his queen moved. The priority of check teaches that when you have two possible captures and wish you could make both of them, you start with whichever one also gives check (if either does). This creates time for you to then play the other one.