The “stay back” part means he doesn’t start moving his center of gravity forward toward home plate until after the knee has peaked and is dropping back down. If you look at video of some of the best (e.g. Ryan, Johnson, etc.) you’ll see that they are already moving forward before the peak of the knee lift.
The “opens up” part means that the front leg immediately opens up instead of leading with the front hip and keeping the front leg closed until right before foot plant and then opening up. Opening up the front leg early runs the risk of opening the hips early. It can also take away the explosiveness of the hip rotation.
So, the way you use your lower half better is to start forward sooner and faster to create more momentum, have a nice knee lift (high or back), lead with the front hip keeping the front foot/leg closed longer before opening it up right before foot plant.
By starting forward sooner and getting going faster, you create more momentum which translates into energy available to put into the ball (assuming efficient energy transfer up the body which requires good mechanics and timing). The more energy the lower half creates and gets transferred up the chain, the less energy the arm itself has to try to generate to make up for doing otherwise. In other words, less stress on the arm while still throwing hard.