early 15c., "the bringing of something to bear on something else," from Old French aplicacion (14c.), from Latin applicationem (nominative applicatio) "a joining to, an attaching oneself to; relation of a client to a patron," noun of action from past-participle stem of applicare "attach to, join, connect," from ad "to" (see ad-) + plicare "to fold" (from PIE root *plek- "to plait").
Meaning "sincere hard effort" is from c. 1600. Meaning "a formal request to be hired for a job or paid position" is by 1851. Computer sense "program designed to carry out specific tasks or solve specific problems within a larger system" is a shortening of application program (1969).