Black’s rook on e8 is doing two jobs. It defends the bishop on e7, and it is the only thing standing between the white rooks and a mate on the back rank. One rook, two jobs, and White gets to choose which one it fails at.
7 
2 
d e 
g 1.Rxe7 and Black is stuck. Take back with 1…Rxe7 and the back rank is empty: 2.Rd8+ Re8 3.Rxe8 is mate, with the king still boxed in by his own pawns on f7, g7 and h7. Leave the bishop and Black is simply a piece down. The rook was overloaded, and asking it to do both jobs at once was the whole combination.
One defender, two jobs
Nothing about that position looks broken. Black has the same material, the pieces are on sensible squares, and there is no pin, no fork and no loose piece hanging. That is the point. An overload is invisible in a way a hanging piece is not, because the defender is doing its work right up until the moment you ask it for a second thing.
The jobs come in a few flavours. Guarding a piece. Guarding a square the enemy queen wants. Holding a file or a rank. Stopping a pawn from promoting. Any two of those on the same piece and you have a target.
I lost a game to this at fifteen and still remember the shape: my queen was defending my knight and covering g7, and my opponent took the knight. When I took back, mate arrived on g7.
The question that finds it
In your own games, ask it out loud at the end of each opponent move: what is that piece doing? Not where it stands, what it is doing. If the answer has an “and” in it, look for a way to make one half impossible.
That means a capture, usually. Take the piece it defends, take on the square it guards, or attack it with something it must answer. The deflection puzzles are built almost entirely from this one question, and after two hundred of them you start hearing the “and” without trying.
The defensive half is the same trick in reverse. When your own back rank is bare and a rook is holding it, that rook is not free to do anything else, and the cheapest fix in chess is a pawn to h6. Two seconds, and a whole family of accidents stops existing. There is more on that under back-rank mate.