They are merely signposts for a melodic line. Dizzy suggests going to the piano, which the great majority of jazz musicians do. This not only allows you to see the harmony, but to hear the sounds, which is really what we are talking about. Finally, there is rhythm, which as I said before should be, at least, rated higher than chords. Dizzy points out that without a rhythmic sense it would cancel all the other things.
Sense is a great word for what's needed here.
Your understanding of rhythm must be very intuitive as rhythm is the most primal motivation we have. The rhythm of your heartbeat, walk, your regular schedule, or your groove is not simply metrical. The, rhythm of your life and your music must swing, in other words develop a kinetic energy of its own. This can be directly communicated to others in a big and contagious way. Feeling and sincerity for what you are doing are also important and may come under the category of communication.