Old English dæg "day," also "lifetime," from Proto-Germanic *dagaz (cf. Old Saxon, Middle Dutch, Dutch dag, Old Frisian dei, Old High German tag, German Tag, Old Norse dagr, Gothic dags), from PIE *dhegh-.
Not considered to be related to Latin dies (see diurnal), but rather to Sanskrit dah "to burn," Lithuanian dagas "hot season," Old Prussian dagis "summer." Meaning originally, in English, "the daylight hours;" expanded to mean "the 24-hour period" in late Anglo-Saxon times. Day off first recorded 1883; day-tripper first recorded 1897. The days in nowadays, etc. is a relic of the Old English and Middle English use of the adverbial genitive.