Jazz is not easily boiled down to any one element but when you get right down to it, learning to play jazz is largely about learning how to listen. Really listen, hard, to many things simultaneously while making spontaneous decisions based on what you’re hearing. This is true of all music to some extent but especially so with jazz because it’s so unscripted: there’s often very little on paper to tell you what to play or how to play it, or when. The best jazz is like a coherent conversation between musicians using sounds instead of words, and what makes it coherent – or not – is whether the “conversationalists” are not only speaking the same language, but also really listening to one another.
As a player you have to learn to divide your ear to monitor many aspects at once: the form and structure of the tune being played; the melody, which you try to hold in your ear even after it’s been abandoned; the harmony and its variations; the dynamics; the rhythmic pressure/development and other minutiae; all while trying to hear the big picture, the overall arc of a performance. You have to listen to yourself closely, but also to what everyone else is doing. But while doing all this listening you also have to act and react instantaneously – to not only listen hard, but fast. Hesitate, even for a second, and you’re lost.