The hand-release push up is just a variation of the standard push up. You will commonly see hand-release push ups programmed in certain CrossFit workouts or as part of the Army Combat Fitness Test.
The purpose of the hand-release push up is to ensure that the push up is being performed the correct way. You cannot cheat your way through this movement. Each rep starts from a "dead" or static stop which means you don't get to utilize the stretch reflex that you may get doing the standard push up.
So, if you're bored with your regular push ups or you'd like to challenge yourself with something new, give the hand-release push up a try.
Refer to our page on push ups for a refresher on how to do a proper push up. The difference here is that when you lower your chest to the ground, you lift your hands up off of the ground for a quick moment.
Once you've done this, place your hands back where they were on the ground and push back up into the top of the push up position. Once you've reached the top with your arms fully extended, you have completed one rep.