Short for 'Noble Exchange'. CCP's ill-fated first iteration of the in-game store where goods could be purchased. A paucity of useful items, together with some offensively priced items, and the fear that this would lead to pay-to-win features, to be introduced to EVE, was the precursor of a player riot.
The NEX, now NES, uses a new form of currency other than ISK or PLEX. It uses 'Aurum' [after the latin word for Gold] which can only be purchased with real money or PLEX, which also can be bought with real money.
The NES is the only place where Aurum can be used.