It lets you break the image into pieces. It's like being able to make multiple, persistant marquee selections and manipulate them individually.
I never use it in Photoshop, but in ImageReady, you define slices so you can save the page as HTML and each slice becomes a separate image. It's good for breaking down an image into sub-images, allowing for better filesize optimization. For example, if a large image has an area that is mostly solid color, then you can create a slice for that region and set it to be saved as a gif rather than a jpg.