Eye of the Storm is the new battleground introduced with the Burning Crusade expansion. It is an amalgamation of Arathi Basin and Warsong Gulch.
Aim
The aim is to accrue 2000 points before the opposition does. There are two methods for achieving this. Holding Bases, much like nodes in Arathi, and capturing the flag, like in Warsong Gulch.
Strategies
There are 4 nodes, in a rough rectangle. The centre of the map is where the flag is located. To capture a node, your faction must be the dominant faction in the area – which will bring up a progress bar, similar to any of the Outland PvP objectives. Once you have a node under your control, you can capture the flag back at the node, by bringing it back to a circle on the ground.

It is very important to capture and hold nodes. A common mistake teams make is to fight over the middle ground. This is where the flag pops – but it is much more important to control nodes than to be dominate the middle.
When players die, they will respawn at one of the nodes they control. Therefore it is vital to control the nodes. If you can capture all 4, players will respawn where they first appear. This is a very difficult position to respawn in. There is only one way out, and it is easy to congregate at the bottom of the spawn point. Capturing the flag gives points, but so does holding nodes, just like in AB.
Once the bubble disappears, move half your team to each of the two closest nodes. Once you have captured the nodes, move on to the two across the bridge from there. If you can capture all 4, you will put the opposition at a significant disadvantage from the very beginning. From there you can easily capture the flag at will.