also busy work, "work done simply to keep one occupied," 1884, American English, originally in primary education, from busy (adj.) + work (n.).

How to keep little children busy while not reciting, is the despair of many a teacher. Miss Goodyear solves the problem by introducing a modification of the kindergarten occupations, which she denominates "busy work." Tablets, rings, slats, weaving, and the like, drawing, writing, all are laid under contribution. In this way the interest of the little folk is aroused and directed. ["Annual Report of the State Superintendent of Education, of the State of South Carolina," 1886]

Old English butan, buton "unless; with the exception of; without, outside," from West Germanic *be-utan, a compound of *be- "by" (see by) + *utana "out, outside; from without," from ut "out" (see out (adv.)). Not used as a conjunction until late Old English, "on the contrary." Senses attested in early Middle English include "however, yet; no more than." As an introductory expression, early 13c. As a noun, "an objection, an exception" from late 14c.

Som man preiseth his neighebore by a wikked entente, foralwey he maketh a 'but' at the laste ende, that is digne of moore blame than worth is al the preisynge. [Chaucer, "Parson's Tale"]