Maggie's Farm

The Bench is one of the Big Five strength-conditioners. To make your time on the bench more productive and more of a multi-muscle stress, do not just muscle the bar up with your arms. Engage your back muscles too.

You do this by arching your upper back and raising your chest (while keeping butt on bench) as you lower the bar to your chest, then flattening your upper back against the bench during the press. While this will help you move more weight over time, what matters more is that it stresses more muscle groups in the same exertion.

Remember that eccentric exertion, aka "negatives,"  are a valuable component of strength conditioning.

This guy tries to explain it: