The above example shows a C7 going to a Gb7 with Db in the bass. Notice that the Bb and the E appear in both chords. That shows the tritone substitution in action. Also the roots of the two chords are a tritone apart. The two chords can function as the same chord, as shown here:
This has enormous implications for improvising. You can choose scales, arpeggios and licks based on the tritone sub. Here's an example:
Instead of G7 and Db7 above, try playing the lick over Dmi7 and G7b9 and see what you get. In other words, a lick based on a tritone sub sounds especially effective over an altered chord. Here is a line based on the D dorian and Db Mixolydian (tritone sub of G Mixolydian) scales. Check it out.
You can see how the tritone substitution can open huge areas of exploration for your improvising. Try it out and we'll be back soon with more examples.