I love the Battlegrounds. In my mind, it's the halfway point between general world PvP (no objectives), which is a free-for-all, anything goes brawl and Arenas, which is a tightly controlled deathmatch environment. The former epitomizes war in its absolute sense -- no controls or limits for balance in terms of numbers or levels or gear, there are no match start times, and there is no set ending. Think of old school Hillsbrad PvP or run-of-the-mill gankage. It's pure conflict with no constraints. The flip side is Arenas, which is as close as the game can get to a sport, as much as possible trying to pit evenly matched teams against each other.
Battlegrounds are the compromise. The format tries (admittedly sometimes unsuccessfully) to control numbers as well as limit the instances where organized teams are matched against a rabble of random players. Brackets limit level disparity and map objectives give direction to the encounters. Battleground objectives give a little flavor to the PvP, although players can treat it like a deathmatch, too, sometimes at the expense of prolonging or losing the game. Solo players -- playing any class of any spec -- can have a go at it and come away with a good experience, as Battlegrounds aren't as harsh as Arenas in terms of team composition. In Patch 3.2, Blizzard plans to introduce a new Battleground, which should be pretty exciting. The fun doesn't stop there, either, as it looks like developers are at work on even cooler things for this aspect of the game.