"person who receives guests," especially for pay, late 13c., from Old French oste, hoste "guest, host, hostess, landlord" (12c., Modern French hôte), from Latin hospitem (nominative hospes) "guest, stranger, sojourner, visitor (hence also 'foreigner')," also "host; one bound by ties of hospitality."
This appears to be from PIE *ghos-pot-, a compound meaning "guest-master" (compare Old Church Slavonic gospodi "lord, master," literally "lord of strangers"), from the roots *ghos-ti- "stranger, guest, host" and *poti- "powerful; lord." The etymological notion is of someone "with whom one has reciprocal duties of hospitality" [Watkins]. The biological sense of "animal or plant having a parasite" is from 1857.
Old English Wielisc, Wylisc (West Saxon), Welisc, Wælisc (Anglian and Kentish) "foreign; British (not Anglo-Saxon), Welsh; not free, servile," from Wealh, Walh "Celt, Briton, Welshman, non-Germanic foreigner;" in Tolkien's definition, "common Gmc. name for a man of what we should call Celtic speech," but also applied in Germanic languages to speakers of Latin, hence Old High German Walh, Walah "Celt, Roman, Gaulish," and Old Norse Val-land "France," Valir "Gauls, non-Germanic inhabitants of France" (Danish vælsk "Italian, French, southern"); from Proto-Germanic *Walkhiskaz, from a Celtic tribal name represented by Latin Volcæ (Caesar) "ancient Celtic tribe in southern Gaul."
As a noun, "the Britons," also "the Welsh language," both from Old English. The word survives in Wales, Cornwall, Walloon, walnut, and in surnames Walsh and Wallace. Borrowed in Old Church Slavonic as vlachu, and applied to the Rumanians, hence Wallachia. Among the English, Welsh was used disparagingly of inferior or substitute things (such as Welsh cricket "louse" (1590s); Welsh comb "thumb and four fingers" (1796), and compare welch (v.)). Welsh rabbit is from 1725, also perverted by folk-etymology as Welsh rarebit (1785).