The triplet is a fundamental subdivision in jazz. It’s normally thought to provide the essential swing feel (even though the straight-eighth feel predominates at faster tempos). The most common example in drumming is the ride-cymbal beat (Ex. 1). Most comping vocabulary in jazz relates to the easy, natural flow of Ex. 2.
The off-beat triplet provides a terrific means to inject rhythmic tension because it goes against the 4/4 grain. Play Ex. 3 using two hands, and then play the off-beats with just the left hand (Ex. 4), combined with the ride and hi-hat from Ex. 1. Also try separately practicing the bass drum (Ex. 5) and hi-hat (Ex. 6) while playing the ride pattern. Off-beat triplets can begin and end anywhere in the bar, although the final triplet of beat 4 often works best (for starting and stopping à la Philly Joe Jones). Use in your music as desired.