People who want to know about the expansion in general should also look at the standard Burning Crusade edition. I'm just going to add some information here about what's different with the Collector's Edition.
The most important thing to know is that each copy of the expansion, for either version, comes with a key code that you have to put in to upgrade your account. Without the code, you won't be able to access the new content even if you have the software installed. [Edit: As of January 22, 2007 Blizzard has announced on their forums that they're working on allowing players who already upgraded using the basic expansion to then also upgrade using the collector's edition in order to get the limited edition pet. You'll have to call Blizzard's billing service line with the unused collector's edition expansion key, so it's slightly more work than upgrading directly with the CE, but it can now be done.]
The only real difference between the versions so far as playing the actual game goes, is that those who buy the CE will receive a special pet called a netherwhelp on all of their characters. It's basically a baby version of the flying mounts available in Outland.
Most of the benefit of this version is outside of the game. You get a nicer box with it, of course. Inside that box you'll find that you get the game in both CD (4 of them) form, and DVD form (just 1, so you don't have to mess around with changing the one in the drive).
In addition to the game itself, you get a number of other items. There's a very nice mousepad with a map of Outland on it (though I've heard that the glossy surface works poorly with laser mice). There's a hardcover book of art from World of Warcraft. They include some cards from the WoW collectible card game, along with directions for those who want to play. If you love the music you find in Burning Crusade, you'll also be happy to see that there's a soundtrack included in the box. Finally, there's an additional DVD that contains two hours of behind the scenes material, including things like interviews.
Keep in mind, however, that the only in game benefit is the pet. If you don't want the pet but want everything else, you'll probably be able to get the other items cheaply from someone who wanted the pet and not the rest. Or, you could buy the set and then sell the activation code to someone who wants the pet, while you keep the extra items for yourself.
Due to the need for an activation code, though, be careful about buying this item used. Make sure that you confirm with the seller that the activation code in their set has NOT been used, because it can only be used to upgrade a single account. After that, even if you use the software in the box to upgrade the version on your computer, you WILL NOT have access to the new content. An expansion upgrade code is REQUIRED and it must be one that has never been used.