while (n.) Look up while at Dictionary.com
Old English hwile, accusative of hwil "a space of time," from Proto-Germanic *hwilo (cognates: Old Saxon hwil, Old Frisian hwile, Old High German hwila, German Weile, Gothic hveila "space of time, while"), originally "rest" (compare Old Norse hvila "bed," hvild "rest"), from PIE *kwi-lo-, suffixed form of root *kweie- (2) "to rest" (cognates: Avestan shaitish "joy," Old Persian šiyatish "joy," Latin quies "rest, repose, quiet," Old Church Slavonic po-koji "rest"). Notion of "period of rest" became in Germanic "period of time."

Now largely superseded by time except in formulaic constructions (such as all the while). Middle English sense of "short space of time spent in doing something" now only preserved in worthwhile and phrases such as worth (one's) while. As a conjunction, "during or in the time that; as long as" (late Old English), it represents Old English þa hwile þe, literally "the while that." Form whiles is recorded from early 13c.; whilst is from late 14c., with excrescent -st as in amongst, amidst. Service while-you-wait is attested from 1911.
while (v.) Look up while at Dictionary.com
"to cause (time) to pass (without dullness)," 1630s, earlier "to occupy or engage (someone or something) for a period of time" (c.1600), new formation from while (n.), not considered to be from Middle English hwulen "to have leisure," which is from a Germanic verb form of while (n.) (compare German weilen "to stay, linger"). An association with phrases such as Shakespearean beguile the day, Latin diem decipere, French tromper le temps "has led to the substitution of WILE v by some modern writers" [OED] (see wile (v.)).