This is explained a bit in this video
The idea as I understand it relates to thinking about the femur as a lever. There is a hinge at the knee and hip. To move efficiently you want both ends of the lever to be moving as the same speed. For example in a squat your knee and hip should start moving and finish moving at the same time. That makes the lever more efficient? If the knee locks but the hip keeps going for example or vice versa then the lever is not operating as efficiently as it could do with matched speeds.
mc explains it thus:
Bone rhythm effectively means that one gets the top and bottom of a prime mover bone move at the same speed in an action. In a push up, we see this when the shoulder and the elbow finish the move together - both in the press up and in the descent. This move tune alone is worth the price of admission. In the DVD both upper and lower body drills are taught, as well as how to cue another person to get the ryhthm.
I am pondering how /if this fits with Bill DeSimone's approach in Moment Arm Exercise. Bill uses some limited ranges of motion to address the levers, focussing on matching maximum moment arm with the position of the muscles maximum strength. I wonder if you could see the limited range of motion as facilitating better bone rhythm?