Well, WoW is not about story.
WoW is a Roleplaying Game
it is by its very nature about story
The story writing just got nerfed
The basic story is, they arent officially at war, but the people of the two factions have such long traditions of hate for one another (except for the Night Elves, Dreanei and technically the Forsaken) that on an individual basis, they act as if they were at war. The Battlegrounds are also isolated temperments, generally the factions do not behave in that way towards eachother
HOWEVER.... Recently the Horde and Alliance have reentered a state of open war, the story (the basis, anyways) is:
The Alliance and Horde are in Northrend. The Forsaken release the new plague. The Alliance ASWELL as the Scourge are destroyed by it. Varimathras stages a coup in the Undercity. Varian, recently returned, show up in the UC and bitchslaps Thrall (hes not only mad because of the treachery, but also because some dude died... good friend...at the hands of the Horde). He boogies off pretty quick, Thrall and Sylvanas claim to have had no knowledge of the real effects of the plague or the "coup".
A Summary:
Varain is pissed. Thrall is sad. Jaina saved the day again. None like Sylvanas. Varimathras was spanked.