A Push Press is a progression of the overhead press in which a forceful hip drive is used to aid in getting the load overhead. The next progression up from the push press is the push jerk (see video below).
When done properly, the bar moves in a perfectly vertical plane only, which is the most efficient path. To do this, one must 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". Finally, some other key points to address is the importance of having active shoulders, a strong jump stance with the feet directly under the hips, and a small dip to facilitate the drive of the load upwards. Note that the dip is not so low as to be a front squat, which takes away the stretch that helps drive the force.
The Push Press is one of the nine foundational movements of the CrossFit Methodology.