Spots and stripes are both a type of camouflage called disruptive coloration. The spots and stripes break up what would otherwise be a solid color, making the animal look less like a large target and help it blend into the background. Spots are especially useful for hiding in long grass.

Another way that spots and stripes work as camouflage is by confusing the predator. If a predator spots a zebra, say, and recognizes it as prey, chances are the predator will fixate on the stripes as it stalks the zebra.
When the zebra senses the predator and runs away, the white and black stripes blur into a gray background and the predator immediately looses its target. Predators are usually very good at sensing movement, but the initial split second of confusion may be enough time to allow the zebra to escape. If you ever get a chance to go snorkeling or diving in tropical waters, you'll notice that most of the colorful butterfly fish on coral reefs have disruptive camouflage (either spots or stripes or both).

Lastly, a stripe covering the eye and lots of dark spots on the body help hide the eyes of prey, so the predator may become confused about which end is the head. Why would this be a good thing to hide from the predator?