From etymonline:
"to crush, squeeze," early 14c., squachen, from Old French esquacher, variant of esquasser, escasser, escachier "to crush, shatter, destroy, break," from Vulgar Latin *exquassare, from Latin ex "out" (see ex-) + quassare "to shatter" (see quash "to crush").
Squash was originally a drink made from crushed fruit and must have turned into a concentrate somewhere down the line.
Nice.