"cylinder or frame turning on an axis," especially one on which thread, yarn, string, etc. is wound after being spun, Middle English rele, from late Old English reol, hreol "reel for winding thread," from Proto-Germanic *hrehulaz; probably related to hrægel "garment," and Old Norse hræll "spindle" (from PIE *krek- "to weave, beat;" source also of Greek krokus "nap of cloth").
Specifically of the fishing rod attachment from 1726. Of a film projector apparatus from 1896, hence in movie jargon "a length of film wound on one reel" as a part of a whole motion picture. With a number (two-reeler, typical of snort comedy, etc.) indicating film length (by 1916). Reel-to-reel as a type of tape deck is attested from 1958.
late 14c., relen, "to whirl about, turn around," also "sway, swing, rock, become unsteady," probably from reel (n.1), on the notion of "spinning." The sense of "sway or stagger as a result of a blow, etc." is from late 15c. The meaning "walk in a swaying or staggering manner," as one intoxicated might, is from c. 1600. Of the mind or head "be affected by a whirling or dizzy sensation, become giddy," from 1796 (reeling, in reference to mental processes, is from mid-15c.). Related: Reeled; reeling.
late 14c., relen, "to wind on a reel, wind (yarn, thread, etc.) on a reel," from reel (n.1). Fishing sense of "wind (the line) on a reel" is from 1849.
The verbal phrase reel off "recite without pause or effort" is from 1837, perhaps an image from spinning (reel off is attested by 1801 as "wind off on a reel"), but in early 19c. it had a particular sense in silk manufacture. To reel (something) in "recover by winding on the reel after the line has been played" (1881) is an image from fishing. Related: Reeled; reeling.