Old English niehsta, nyhsta (West Saxon), nesta (Anglian) "nearest, closest," superlative of neah (West Saxon), neh (Anglian) "nigh;" from Proto-Germanic *nekh- "near" + superlative suffix *-istaz. Cognate with Old Norse næstr, Dutch naast "next," Old High German nahisto "neighbor," German nächst "next." Adverbial and prepositional use from c.1200. Phrase the next person "a typical person" is from 1857.
To become familiar with someone, esp in view of sexual favors: I'm telling you, you were liable to get next to that broad (1896+)