1868, earlier alla capella (1824), from Italian, "in the style of Church music, in the manner of the chapel," literally "according to the chapel," from cappella "chapel" (see chapel). Originally in reference to older church music (pre-1600) which was written for unaccompanied voices; applied 20c. to unaccompanied vocal music generally. Italian a is from Latin ad "to, toward; for; according to" (see ad-); alla is a la "to the." Sometimes in the Latin form a capella.
Also denoting "that instruments are to play in unison with the voices, or that one part is to be played by a number instruments." ["Chambers's Encyclopaedia," 1868]
You are not the first person puzzled by the expression "A Capella," or, at any rate, unable to understand it should signify the exact reverse of what it literally does signify. The chorales in oratorios were invariably accompanied, either by double-bass or the whole band. Hence they were, with perfect correctness, said to be performed "a capella." But, as other chorales, sung as part of the church service, were written in the same and simple style the expression "a capella" came in time to be applied to them also, despite their being sung without any instrumental accompaniment whatever. [The Music World, Sept. 11, 1875]
northern constellation, from Latin auriga "a charioteer, driver," also the name of the constellation, which is often explained as from aureae "reins, bridle of a horse" (from os, genitive oris, "mouth;" see oral) + agere "set in motion, drive, lead" (from PIE root *ag- "to drive, draw out or forth, move"). Its bright star is Capella.
early 13c., "subordinate place of worship added to or forming part of a large church or cathedral, separately dedicated and devoted to special services," from Old French chapele (12c., Modern French chapelle), from Medieval Latin capella, cappella "chapel, sanctuary for relics," literally "little cape," diminutive of Late Latin cappa "cape" (see cap (n.)).
By tradition, the name is originally in reference to the sanctuary in France in which the miraculous cape of St. Martin of Tours, patron saint of France, was preserved. (While serving Rome as a soldier deployed in Gaul, Martin cut his military coat in half to share it with a ragged beggar. That night, Martin dreamed Christ wearing the half-cloak; the half Martin kept was the relic.) The other theory is that it comes from Medieval Latin capella in a literal sense of "canopy, hood" and is a reference to the "covering" of the altar when Mass is said.
The word spread to most European languages (German Kapelle, Italian cappella, etc.). In English from 17c. it was used also of places of worship other than those of the established church.