Engadget posts a hands on video of the iPhone 4 in action with ngmoco’s new Eliminate: Gun Range game that supports the gyroscope.
As you can see in the video, the game is a gallery shooter but the use of the gyroscope can add more precision to the movements. (Sorry, not viewable on iPhone)
Not entirely well shown in the video is the fact that you can also move the phone in 3d space to change your aim. While some of the same gameplay can be reproduced with the accelerometers, the gyroscope adds more precision and also allows you to, for example, translate the device in 3d space. Rotating your body to the left, for example, will shift your aim accordingly.