early 13c., from Old French bolir "boil, bubble up, ferment, gush" (12c., Modern French bouillir), from Latin bullire "to bubble, seethe," from PIE base *beu- "to swell" (see bull (n.2)). The native word is seethe. Figurative sense of "to agitate the feelings" is from 1640s.
Related: Boiled; boiling. Boiling point is recorded from 1773.