The improvisation is a kind of subversive play. One deliberately contorts the melody, creating something different and personal. A good chorus is intellectually engaging, a statement of the player's view of the world. The solo should also resonate to the underlying feel of the tune. Not a few songs evoke the hardships and travails of the human experience, as well as the shared aspiration for overcoming them.
Jazz is a music of protest and possibility.
For me, it offers succor and relief from the oppressive aspects of my medical work. Without it, I might well become inured, hardened, and less able to feel for my patients and their families. I sense that my feelings are also felt by others, by band members as well as the audience. Mostly I play with my eyes closed, but sometimes when my feelings almost overwhelm me, I'll open my eyes. Then I see that what I'm feeling is real.