In the sport of football, "escapability" refers to a quarterback's ability to escape pressure from the defense while in the pocket. The term itself comes from former NFL quarterback and well-known analyst Trent Dilfer, and is synonymous with elusiveness and awareness in the pocket.
On passing plays, the offense will usually require the quarterback to step back (or "drop back") in the "pocket" created by the offensive line. If no wide receivers are open, the quarterback needs to get creative, and either escape the pocket before the defenders get to him or throw an incomplete pass.
Seeing as the NFL is currently a pass-heavy league, the ability for a quarterback to escape from pressure is crucial. That being said, many quarterbacks fail to succeed in the NFL due to their tendency to use their legs too much. "Pro-style" quarterbacks who hang in the pocket and exhibit good arm strength are more likely to succeed at the professional level, and are certainly preferred over less-traditional "scrambler" quarterbacks.
If escapability is a quarterback's best trait, it probably will be a problem. That being said, having good escapability is never a bad thing. Legends like Peyton Manning, Tom Brady, and Donovan McNabb are great examples of quarterbacks who exhibit escapability well.