We had some hints that this would happen soon and now WoW Insider has confirmed through anonymous sources that the next expansion, Wrath of the Lich King, is in closed alpha status, and that various players are being invited to check it out, under a strict NDA.

Alpha is part of the software release life cycle -- a software product in development goes from alpha status to beta status (sometimes including a "closed beta," where a limited few are invited to preview and test the software, and an "open beta,", where anyone can download and try out the beta), to "release candidates" and then "gold" (the final version, used to print the media to be available for sale). This doesn't tell us anything about the timing of the expansion's release (especially since Blizzard historically takes their time going through this cycle), but it does tell us that Wrath's content is in a playable and mostly completed form -- quests, game mechanics, and items are in, even if specific flavor text, names, and even textures are not.