1) Lions are color-blind, and need to focus in on one animal to make a kill. The black-and-white striping acts as a defense mechanism. When chased, a dazzle of zebra will run in-and-out together, creating a 'blur' that confuses the color-blind lion.
2) The striping helps to cool the zebra.
3) The striping is like a fingerprint. Each zebra has a different stripe pattern. When a baby is born, the mother walks around it over and over until it learns her unique pattern and knows who mom is.