c. 1400, hobi, "small, active horse," short for hobyn (mid-14c.; late 13c. in Anglo-Latin), probably originally a proper name for a horse (compare dobbin), a diminutive of Robert or Robin. Old French hobi, hobin, once considered possible sources, now are held to be borrowings from English.
The modern sense of "a favorite pursuit, object, or topic" is from 1816, a shortening of hobbyhorse (q.v.) in this sense, which is attested from 1670s. Earlier it meant "a wooden or wickerwork figure of a horse," as a child's toy or a costume in the morris dance, the connecting notion being "activity that doesn't go anywhere." Hobby as a shortening of hobbyhorse also was used in the "morris horse" sense (1760) and the "child's toy horse" sense (1680s).