Old English slæp "sleep, sleepiness, inactivity," from Proto-Germanic *slepaz, from the root of sleep (v.); compare cognate Old Saxon slap, Old Frisian slep, Middle Dutch slæp, Dutch slaap, Old High German slaf, German Schlaf, Gothic sleps.
Personified in English from late 14c., on model of Latin Somnus, Greek Hypnos. Figurative use for "repose of death" was in Old English; to put (an animal) to sleep "kill painlessly" is recorded from 1923 (a similar imagery is in cemetery). Sleep deprivation attested from 1906. Sleep-walker "somnambulist" is attested from 1747; sleep-walking is from 1840. To be able to do something in (one's) sleep "easily" is recorded from 1953.