GSM is mobile communication system. T-Mobile and Cingular uses this system. So if you have their service, your cellphone is most likely a GSM phone. A GSM phone requires a SIM card to work. The SIM card contains your mobile account info. You can use other SIM cards and put them in your phone. As GBZ39 suggested, you can buy a local SIM card in Belize to incur only local charges, not international which is very pricey. You get a local Belize phone number with it, too. However, your GSM phone needs to be unlocked to be able to use other SIM cards.
If you don't have a GSM phone, you can buy them without a contract which is kind of expensive. Maybe you can look on ebay. When buying, make sure the phone is unlocked and has a band of 1900MHz. You can also buy the pre-paid phones (T-Mobile is cheaper). But again, you have to unlock these phones first before you can use it with other SIM cards.