The etymological sense is "bring things in contact with one another." In English, from c. 1400 as "use or employ" something for a certain purpose;" from early 15c. of lotions, plasters, etc., "place in contact with the body," also, of one's mental powers or faculties, "put to work at a task or pursuit." Meaning "seek a job by submitting an application for one" is from 1851. A by-form applicate is recorded from 1530s. Related: Applied; applying.
"work with, practice with persistence, use or employ diligently," late 14c., shortened form of applien "join to, apply" (see apply). The core of this is Latin plicare "to lay, fold, twist," from Proto-Italic *plekt-, from PIE root *plek- "to plait." The sense of "travel regularly, go back and forth over the same course" is attested from 1803, perhaps from earlier sense "steer a course" (1550s). Related: Plied; plies; plying.