The rocking press up is good exercise for the lower and upper arm muscles - chest - shoulder muscles, which can be performed in either a three-quarter or full press up position.
Aim to keep your elbows tucked into your sides throughout the movement, as you lower down to a position whereby your arms are bent to 90 degrees.
Once in this bent position, you will begin the rocking action, by simply pushing your body forward 4 - 6 inches, holding the outer phase for 1 - 2 seconds prior to returning back either to your starting position, or by extending your body back 2 - 4 inches.
You may decide to perform a few forward and back movements prior to straightening your arms and repeating the process, or straightening your arms on every forward / back movement (harder).
Focus on keeping your back straight and horizontal to the floor during the rocking phase.