early 13c. (intransitive) "to bubble up, be in a state of ebullition," especially from heat, from Old French bolir "boil, bubble up, ferment, gush" (12c., Modern French bouillir), from Latin bullire "to bubble, seethe," from PIE *beu- "to swell" (see bull (n.2)). The native word is seethe. Figurative sense, of passions, feelings, etc., "be in an agitated state" is from 1640s.
I am impatient, and my blood boyls high. [Thomas Otway, "Alcibiades," 1675]
Transitive sense "put into a boiling condition, cause to boil" is from early 14c. The noun is from mid-15c. as "an act of boiling," 1813 as "state of boiling." Related: Boiled; boiling. Boiling point "temperature at which a liquid is converted into vapor" is recorded from 1773.
"hard tumor," altered from Middle English bile (Kentish bele), perhaps by association with the verb; from Old English byl, byle "boil, carbuncle," from West Germanic *buljon- "swelling" (source also of Old Frisian bele, Old High German bulia, German Beule). Perhaps ultimately from PIE root *bhel- (2) "to blow, swell," or from *beu- "to grow, swell" (see bull (n.2); also compare boast (n.)). Compare Old Irish bolach "pustule," Gothic ufbauljan "to puff up," Icelandic beyla "hump."