Norrath is the world which serves as the setting for the EverQuest franchise. EverQuest Next, however, is expected to be set in its own version of Norrath which is likely to have many of the same locations and characters as the original Norrath, but the canon may diverge significantly from the previous games in the franchise.
From SOE Live, we learned that EverQuest Next will have all of the original EverQuest zones, including ones we haven't seen in some time, as well as zones completely new to the franchise. Halas, Feerrott, Lavastorm and subterranean Everfrost were all seen in either concept art or screenshots over the keynote presentation.
The original world of Norrath launched with the continents of Antonica, Odus and Faydwyer. Expansions brought new continents, like Kunark and Velious, and the moon, Luclin. Considering how many of the zones we know from the EverQuest franchise to be in EverQuest Next, in addition to new zones, it can be expected that the game will be quite enormous.