Yes. Your computer has a warranty when you purchase it. If you need repairs beyond the warranty period, you need to purchase AppleCare. AppleCare is an extended warranty or insurance against hardware failure.
if you get Applecare make sure it's Applecare by Apple. I accidentally bought extended warranty from maczone that was not by Apple but by a Servicenet (sp?) company. I was not happy to find out months later when I had a problem that it was not Apple's Applecare and I was not satisfied with Servicenet company's service.