Multiple versions of it in Monk's catalogue but this one -- featuring another jazz legend, John Coltrane on the sax solo/melody -- is my favorite.
Not to be too geeky about it, but what made Monk special were all of his eccentricities: dissonant melodies and unexpected chord/mode changes, using flat ninths, flat fifths, unexpected chromatic notes together. I would describe his piano-playing style as "percussive." There's a lot of noise/silence in his key-tickling.
His distinctive look included suits, hats, and sunglasses. He also had an idiosyncratic habit during performances: while other musicians continued playing, Monk would stop, stand up, and dance for a few moments before returning to the piano.
He's also the second-most-recorded jazz composer in the canon, second only to "Sir Duke" Ellington.