c. 1600 (transitive) "to qualify," from Medieval Latin habilitatus, past participle of habilitare, from habile "fit, suitable" (see able). Intransitive meaning "obtain necessary qualifications" is from 1881. Related: Habilitated; habilitation.
"having sufficient power or means," early 14c., from Old French (h)able "capable; fitting, suitable; agile, nimble" (14c.), from Latin habilem, habilis "easily handled, apt," verbal adjective from habere "to hold" (from PIE root *ghabh- "to give or receive").
"Easy to be held," hence "fit for a purpose." The silent h- was dropped in English and resisted academic attempts to restore it 16c.-17c. (see H), but some derivatives (such as habiliment, habilitate) acquired it via French. Able seaman, one able to do any sort of work required on a ship, may be the origin of this:
Able-whackets - A popular sea-game with cards, in which the loser is beaten over the palms of the hands with a handkerchief tightly twisted like a rope. Very popular with horny-fisted sailors. [Smyth, "Sailor's Word-Book," 1867]