Question: why do tritone substitutions work?
Answer: A tritone substitution is taking any dominant 7 chord you see and play another dominant 7 chord that occurs a tritone (#4 aka b5) away from that initial chord. For example: playing Db7 over G7. The reason that this substitution works is that dominant 7 chords with a bass note a tritone apart share the same 3rd and 7th.