This is a form of tritone substitution, and is considered one of the basic substitutions in jazz. The idea is that you replace a chord (typically a dominant chord) with one a tritone away. (Recall: a tritone, TT, is 3 whole steps, which is the distance of either an augmented fourth or a diminished fifth).
The reason this substitution works lies in the symmetry of the TT - it is exactly half an octave, so it is its own inversion. This lends it to a certain ambiguity. Consider the G7 chord (G B D F). There is a TT between the B (the 3rd of the chord) and the F (the 7th of the chord). But there is also a tritone between the F and the B, so we can reimagine the F as the third of some chord, and the B as its seventh (except now we have to call the B a Cb, to reflect that it is a fifth above the F).
The chord for which F is the 3rd and Cb is the 7th is Db7 (Db F Ab Cb), so we can use that chord. Its root happens to be a TT away from our original G7.
The deal with the (b5) being used just makes it even closer to the original chord. This would replace the Ab with Abb, which is the same pitch as G. So this gives us a very ambiguous chord: It's either a G7(b5) or a Db7(b5), but it has the same pitches both ways (just "spelled" differently):
(G B Db F) vs (Db F Abb Cb)