Play-rest is a way of practicing improvising. Basically what you do is pick a tune to improvise over, then determine a pattern of playing/resting. For example, lets say you want to do a pattern of 1-1. You'd play for one measure, rest for 1 measure, and repeat the pattern. The catch is that you can't let yourself play on the "rest" measures. No pickup notes into the "play" measures, no sustaining notes into the "rest" measures etc. Start off with symmetrical patterns (patterns where the number of measures you rest and the number of measures you play add up to an even number). Start off with things like 1-1, 2-2, 4-4, etc. Then go onto things like 1-3, 3-1, etc. Any combination that adds up to an even number.
Then move on to assymetric patterns where the "play" measures and the "rest" measures add up to odd numbers. Things like 1-2, 2-1, 3-2, 6-1, etc. Keep in mind that any pattern you do can (and should) be reversed. This exercise accomplishes a number of things:
-by setting limits for yourself as to when to play, you force yourself to come up with more interesting phrases because you don't have the option of noodling around without direction.
-you learn to listen more to what you are playing and what you are playing over. Especially once you get into the really odd groupings, you'll have to learn to hear the changes rather than find your way in the form by counting. You'll have a hard time counting both where you are at in your play rest pattern and where you are at in the tune.
-for the same reasons as above, you'll find yourself keeping much better track of time. You'll end up trying to count both no matter how hard you try not to (which is a good thing in a sense) and on a subconcious level you become much more in-touch with time
-you'll be listening to everything else happening in the music and the other players can respond to you better. When you rest, if gives you a chance to think about what you just played and how to follow it up. If you are playing with a band or an accompinist, it gives them a chance to interpret and respond to what you play and respond in one way or another. You also get a chance to listen to the groove they are setting and play more accordingly.
-it's a great way to create tension in a solo, especially if you are constantly changing your play-rest pattern as the listener doesn't know what to expect next and will be very attentive
note, that this is more of a practice method than a playing approach. The idea is to practice the hell out of these ideas so that when you are playing you are more aware of the concept and can incorporate hints of it in your playing. I can't imagine ever sitting on a gig going "ok....there's one measure of notes, time to rest for 3....oh shit I played one too many notes.....oh no I only have one more beat to finish this idea...etc.".
For a great example of this, check out Miles' solo on this tune:
[ame]http://youtube.com/watch?v=U4FAKRpUCYY[/ame]
Take note of how he leaves space inbetween his phrases. Obviously, he's not doing a straight "ok....play one measure, rest one, play one, rest one..." but he's making great use of the concept. The space in between phrases is just as important to the solo as the phrases themselves. The song is called So What...off of the Kind of Blue album. Coltranes' solo on this is stellar too and is a great study in a number of soloing concepts.