There are two reasons for Zebras to have evolved stripes.
The first is concealment from and avoidance of predators. Zebras stripes do this in two ways.
Disruptment Camouflage. Normal camouflage works by blending in with or copying the colours and patterns of the surrounds. Obviously the stripes don’t copy the surroundings. Disruptment camouflage works by breaking up the outline of something making it harder to distinguish and therefore identify clearly. See:http://en.wikipedia.org/wiki/Cam…
Personally I found Zebras one of the more difficult animals to learn to distinguish at very long distance when I first began to work in the bush. From very far they can even look like lions with the naked eye. It can also be hard to distinguish one from another when they are in a herd and running.
They other way they work to confound predators is by the use of Motion Dazzle. This works by distorting predator’s ability to effectively judge the animal’s movements and speeds and therefore making it more difficult to catch. See:http://en.wikipedia.org/wiki/Cam…
The second reason that Zebras have evolved stripes is to protect themselves from Parasitic Flies, especially the Tsetse Fly. The biting tsetse fly carries trypanosomes which cause animal trypanosomiasis.
Although there has been much hype recently studies showing that flies might struggle to see Zebra stripes, it was actually well clearly established by the Zimbabwe Veterinary Department decades ago in the work of a man called Ted Davidson.
This is how they discovered it. They were trying to discover what colours would work best for tsetse fly traps (see here tsetse) and tried all sorts of things eventually finding out that the best colour to attract them was electric blue whilst the best colour for them to land on was black. They also tried different patterns and colour combinations and found that weren’t attracted to and didn’t land on Zebra stripes!