The main predator of the zebra is the lion. Lions don't like to hunt in the heat of the day, they prefer sleeping in the shade. They hunt as it gets dark. As the sun goes down the black and white stripes of the zebra help it blend into the tall grass. But the zebra's stripes have another purpose.
Zebras live in herds.
Lions like to pick out one member of the herd that looks weak. When the lion attacks, the zebras start running in all directions. With all those stripes mixing together, its easy for the lion to lose the zebra it picked out of the herd. Sometimes an animal blends best into its environment when it is a solid color. The white fur of the polar bear is perfect for an arctic environment.