What is a pass rush?

A pass rush is the defenses attempt at putting pressure on an opposing team's quarterback. More times than not, it's the defensive team's front four that is responsible for putting pressure on the quarterback. Those four players are known as the defensive line. The two players in the middle are the defensive tackles, usually the meat of the defense. The two guys on the outside are the defensive ends and they are usually the faster of the bunch.

A straight attempt at a pass rush would consist of the two defensive tackles and the two defensive ends rushing towards the quarterback in an attempt to sack him for a loss of yards, but not limited to the four down lineman.
A lot of times, in hopes of adding pressure on the quarterback, defenses will add extra players to the rush scheme, meaning, linebackers, safeties and defensive backs may also get in on the pass rushing.
The reason that defenses rush players from other positions is so to confuse a quarterback's offensive line so that they won't know who to block. It's easy for an offensive lineman to block the four down linemen the entire game. But when three of the down lineman, one linebacker and one defensive back rushes one time and when all four and three linebackers rush the next, offensive line can and will get confused.
Also, sacks aren't the only reason why a team may send pass rush pressure. They also want to get the quarterback in a position where he is hurrying his passes as well as just knocking him down. A productive and effective pass rush can force turnovers as well as bad throws and unforced errors from a quarterback.