Mostly we have concerned ourselves so far in this chapter with cases where an enemy piece is guarding two sensitive points on the board in front of you. But it also is possible to create an overworked piece. You see an enemy piece guarding against mate; so you build an additional mate threat on another square it also protects. It becomes stretched too thin, and then one of the threats works or you win material that your opponent has to sacrifice to save the game.
In this first example you see that you (playing the Black pieces) have a queen close enough to White’s king to menace it. Think more precisely about how it could become a mate threat. If the queen had a supporter attacking h2 or g2, it could mate there. Black could furnish such support with Re2. The rook on e1 obviously seems to prevent such a move, but hold that thought anyway. Now notice that since the king is cornered, Black also has the makings of mate with QxRf1. This, too, is prevented by the rook on e1. Aha: the e1 rook can be overworked; it guards (or will guard) against two mating threats. So you go ahead with Re2, which results in mate one way or another: (a) If White plays RxR, Black plays QxRf1#. (b) If White for some reason plays Rg1, Black plays Qxh2#. (c) If White plays Rf2, Black plays RxRf2 (not RxRe1, since then White has BxR); and now nothing can stop Black from mating with his queen on h2. (White has a couple of futile checks on Black’s back rank that delay matters for a move or two.)
The e1 rook can be understood as overworked in that it guarded both the mating square f1 and also e2, which was a stepping-stone to mate for Black and not guarded by anything else. Another way to look at this position is that Black creates an overworked enemy defender. The e1 rook was frozen in place because it needed to protect f1; once Black sees this, he takes advantage by sticking a rook next to it and creating a fresh mate threat in the process.