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The idea of a chord substitution is to replace one or more chords in a progression with others that have a similar or contrasting meaning.

Bebop improvisors liked especially to add additional pitches (called extensions) to 7th chords (usually the most dissonant chords in their chord progressions) to vary their color and frequently to increase their dissonance.

In a progression like Emi7-A7-D7-Dmi7-G7-C7-FMA7, they might substitute a 7(b5), a 7(b13), a 9 or a 9(#11) among many other possibilities for the original 7 chords. You might end up with a Emi7,A7(b5),D9(#11),Dmi7,G7(b13),C9,FMA7 progression using this palette of substitutions.

Rather than simply adding additional notes to a 7th chord they could also substitute a chord built on a different root that had almost the same harmonic meaning as the original chord.

It was well known among the beboppers that one could substitute a 7th chord whose root was an augmented 4th interval away from the original root of a 7th chord, resulting in a harmonic sensation that listeners readily accepted. They called this a tritone subsitution, because if you traveled up from a pitch by three whole steps, you covered the distance of the augmented 4th interval.

Example of tritone subs in use:

Given a C7-F7-Bb7-Eb7 progression, substitute B7 (a tritone away from the second chord, F7) and A7 (a tritone away from the fourth chord, Eb7) resulting in the transformed progression C7-B7-Bb7-A7.

If you knew a melody that fit the first sequence, you could play it over the transformed sequence and most likely all of the original melody pitches would work in the new setting.