A Push Jerk is a progression of the push press in which a forceful hip drive coupled with a drop under the bar--a catch--is used to aid in getting the load overhead.
The push jerk adds a jump and dip landing to the push press. It takes a lot of practice to get good at this movement and you should train with a dowel or bar every workout as a skill warmup.

Muscle group: Combined

Steps

Move the head back to make room for the bar, then replace the head to the normal position after the bar passes by. The lift is complete when the arms are locked out overhead, with the head "through the window", and the feet are reset into the jump stance (directly under the hips).

Tips

It is important to have active shoulders, and a small dip to facilitate the drive of the load upwards. The drop under the bar makes it so the load doesn't have to travel as far to make the catch easier. Note that the dip is not so low as to be a front squat, which takes away the stretch that helps drive the force up enough to pull underneath it during the catch. It is also common to "jump" the legs from hip width into a squat stance, where the hips are about shoulder width apart.

According to CrossFit, you can typically lift 30% more weight with the push press than with the shoulder press and 30% more with the push jerk than with the push press.

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