c. 1400, apparently from the gerund of the Middle English verb inclen "utter in an undertone, hint at, hint" (mid-14c.), which is of unknown origin; perhaps it is related to Old English inca "doubt, suspicion, question, scruple." However the earliest record of the word is as a nyngkiling; and The Middle English Compendium offers that this is not a misdivision of an inkling but rather suggests the word is a nasalized variant of nikking "a hint, slight indication," gerundive of the Middle English verb nikken "to mark (a text) for correction" (mid-15c.), from nik (n.) "a notch, tally" (see nick (n.)).
early 15c., boh, "A combination of consonant and vowel especially fitted to produce a loud and startling sound" [OED, which compares Latin boare, Greek boaein "to cry aloud, roar, shout"]; as an expression of disapproval, 1884 (n.); hence, the verb meaning "shower (someone) with boos" (1885).
Booing was common late 19c. among London theater audiences and at British political events; in Italy, Parma opera-goers were notorious boo-birds. But the custom seems to have been little-known in America before c. 1910. To say boo "open one's mouth, speak," originally was to say boo to a goose.
To be able to say Bo! to a goose is to be not quite destitute of courage, to have an inkling of spirit, and was probably in the first instance used of children. A little boy who comes across some geese suddenly will find himself hissed at immediately, and a great demonstration of defiance made by them, but if he can pluck up heart to cry 'bo!' loudly and advance upon them, they will retire defeated. The word 'bo' is clearly selected for the sake of the explosiveness of its first letter and the openness and loudness of its vowel. [Walter W. Skeat, "Cry Bo to a Goose," in Notes and Queries, 4th series, vi, Sept. 10, 1870]