Here's the current principle in less intuitive form. Black starts with a pin of White’s bishop by his own. Black’s bishop is loose, so he has to worry about White playing BxB next move; but since his bishop does pin White’s at least for the moment, perhaps Black can take advantage with a cross-pin. Structurally it’s about the same as the previous example, though this time it's a little harder to see because the winning move, Qe2, requires Black’s queen to get behind White’s bishop. Still, you wouldn’t miss it if you were careful to look at all the lines leading away from the pinned bishop, and then likewise careful to check whether any of your pieces can get on the opposite side of the bishop from its queen.

What will White play in reply? You might reasonably worry about QxBa3. But remember that when you have a cross-pin like this, either of your pinning pieces can capture the pinned piece and give check at the same time. That’s important because checks seize the initiative from your opponent. If White does play QxBa3, Black thus has QxB+. White is forced to play Ka1; and with Black’s queen and bishop now lined up, Qb1# then is mate.