Here's a simple tune. The first half of the melody simply teeter-totters the G minor scale, while the second half outlines four ascending chords. The solo section consists of a basic minor ii-V7 progression. Awesome! We officially have a tune and a jam! It's that easy.
So, let's discuss what makes simplicity interesting. In this particular case, rhythm is the key factor. In the melody, syncopation is used to contrast the two sections. In the trombone solo, the rhythmic phrasing appears to be the only variable. The shapes of the phrases consistently seem to leap upward and then descend down the scales (C bebop, G blues). The harmony tends to stay within these scales as well, although he does like to make use of those A's, it's still mainly a diatonic passage. The varying rhythms, however, mark the clear boundaries to his phrases, like using "quotation marks" to indicate separate thoughts or ideas.
With each successive phrase, his rhythms become more complex and lead up to his 1-2 punch: technicality and power. The superhuman sextuplets appear to be effortless, and set up the powerful high G. This knock-out blow also contrasts the previous phrases with simple rhythms. He then takes one last phrase to cap it all off. It doesn't require a genius with trombone blog to figure this out: a lot of complex ideas can be expressed simplistically. It just requires a creative mediator to make it funky.
And a side thought about those sextuplets: in his previously solos, Shorty's used the sextuplet rhythms to arpeggiate a chord, such as a G major triad in 4th position or an Ab in 3rd. Sure, it makes sense. Here, however, he plays a C, D, and F. The best explanation that I could come up with is that this riff comes from the guitar (as it plays easily using a hammer-on technique) and that Shorty has a good ear for borrowing from his rock influences.
Here's a YouTube video of Trombone Shorty playing AC/DC's "Back In Black."
Recommended Reading: Causing a Scene: Extraordinary Pranks in Ordinary Places with Improv Everywhere by Charlie Todd and Alex Scordelis. Published by Harper Collins.