AppleCare is the brand name for various warranties on Apple Mac computers, iPods and peripherals. It generally covers 1 year of repair service and 90 days phone support out of the box for most products, which can then be both be extended anytime within the first year to a 3 year period at additional cost.
AppleCare is not cheap, but is like insurance or any other gamble: If your Mac never breaks, AppleCare was expensive and useless. If your mac has any hardware problem, it will probably pay off, because official Apple Service centers can not usually repair components, but must instead replace the bad module. On Macbook laptops, the only "module" is pretty much the motherboard, for $1000. However, AppleCare does not cover computers that get wet. So, even with AppleCare, you are out of luck if you spill something on your laptop or drop it and break it.
The college has generally been buying AppleCare for all Macs we own, but we are currently (Jan 2008) reconsidering this policy since the cost vs. rate of covered failures is not very good. OTOH, it is really handy if you have a hard to reproduce problem and you can just have them fix it.
The phone number for AppleCare's Education division is 1-800-800-2775. (For college owned machines, we have a "Service Account" so they will send us replacement parts without needing a credit card.