Warcraft III is Blizzard's first foray into the 3D World. It will be an RTS with some elements of RPG such as heroes with XP and Inventory and NPC's like merchants and mercenaries which will be important in every game. It was formerly labelled an RPS, Role Playing Strategy, but Blizzard apparently dropped some of the RPG elements and went back to calling it an RTS.
The game is set one generation after the orcs first invaded Azeroth and 15 years after the end of Warcraft II. It assumes that the humans won in Warcraft II - The Tides of Darkness (which in turn assumes that the orcs won Warcraft I). There are still orcs in Azeroth but there is now relative peace. The orcs are being united under Thrall (from the cancelled Warcraft Adventures game) and returning to their original shamanistic, noble, and not-so-evil culture (it turns out that all their evilness and invading Azerothness came from the corruption of the Burning Legion), while the Alliance is suffering from infighting and disunity.
One day multitudes of fiery meteors rain from the sky. These are carrying the invasion force of the Burning Legion, the Daemons from the other two Warcraft games. Since they failed to destroy the world by proxy through the orcs, they attack themselves bringing with them the Scourge, an undead army formed from the orcs who went into the Twisting Nether at the end of Beyond The Dark Portal. (No mention is made of what happened to the humans who went into the Twisting Nether.)
There are also Night Elves, the first race to arise in Azeroth. 10,000 years before, they had unleashed the Burning Legion into the world through unrestrained use of magic, and barely survived. Their homeland of Kalimdor was destroyed in the battles. They became secretive and hid themselves off from the rest of the world, and outlawed the use of magic. The elves in Warcraft II were exiled from the Night Elves for using magic. Now with the return of the Burning Legion, the Night Elves have to fight again.
There were originally going to be six playable races, but one was dropped for storyline reasons, and the Burning Legion was removed as a playable race because it was too hard to balance them while maintaining their flavor as an extremely powerful invading demon army.
The game is 3D, but has a fixed camera angle (IMO a mistake - if you have played Homeworld a good deal of the fun was viewing the battle from different angles and close-ups) and an interface similar to the Starcraft and Warcraft interfaces. The resources are gold, mined from gold mines, and lumber, from trees of course. (There used to be "mana stones" obtained by interaction with (killing) neutral units, but these were removed. Lumber was also removed but has been replaced.) Trees can also be cleared or grown for strategic reasons. There are no sea units (Blizzard's other mistake - naval units added a great deal to Warcraft II that will be missing now) but there are air units. The game will have weather effects (that are only visual) and a day/night cycle (that can affect the gameplay).
There are some very good cinematics at http://www.blizzard.com/war3/movies/. Be sure to download the 2001 E3 trailer, which I think has the best CG work I have ever seen, achieving photorealism in a few places. Unfortunately, the gameplay movie is crap. It is about 320x240 and compressed to the point that you can barely make anything out.