Counterpoint, or "the art or technique of setting, writing, or playing a melody or melodies in conjunction with another," has been around in jazz since the very beginning. Just listen to any early New Orleans jazz performance and you'll hear trumpet, clarinet, and trombone melodies weaving in and out of each other in contrapuntal ways. But the swing era of the 1930s brought with it an emphasis on soloing as well and an ensemble concept that was largely based on instruments playing in rhythmic unison, at least within their own sections. So jazz counterpoint largely fell by the wayside.
A few musicians kept the flame alive, largely through an interest in Bach. Foremost among these musicians was the pianist/composer John Lewis. Lewis composed and arranged large-scale works for his group, The Modern Jazz Quartet that incorporated fugal and imitative techniques in a way that was reminiscent of Bach.
Pianists such as Bud Powell, Keith Jarrett and Brad Mehldau have brought a contrapuntal approach into some of their improvisations, with each hand playing its own melody at the same time.
Learning to improvise counterpoint is a wonderful way to bring a new dimension into your own jazz piano playing. There are as many ways you can do this as there are types of counterpoint: strict imitation, free counterpoint, fugal techniques, not-against-note, etc. Pick a jazz tune and see where this leads you. (Your left hand will be forever grateful to you. It finally has something to do!!!)
Here's a video I made to get you started, using the tune "Over The Rainbow" as an example. Watch my performance a few times until you get the basic idea, and then go to your piano and try it yourself. Don't go for a "perfect" performance. Remember, you're trying something that you've probably never done before. Stick with it, though, and you'll get more and more out of it as you go deeper into the whole area of counterpoint. And if you want some more inspiration, you can always turn back to the master, old J.S. Bach himself. Have fun!
Get my free ebook: Left Hand Techniques for Jazz Piano
You'll also get my weekly jazz newsletter with practice tips and inspiration