What is a SIM card, you may wonder? SIM stands for Subscriber Identity Module. The SIM card is also known as a Smart Card. The SIM card is the "brain" of your phone, and when a call is sent out to your phone, it is the information contained in your SIM card that identifies your phone as the call's destination. In a sense, the SIM card makes your phone YOUR PHONE, rather than A PHONE. All of your user information is contained therein.
A SIM card, or Smart Card, can be removed from your phone. If you are traveling overseas, you may want to use your trusty cellular phone, but not use the service you typically use, as it would incur pricey long-distance or roaming charges. In this case, you can purchase a pay-as-you-go or monthly plan upon your arrival at whatever destination you choose. You will be given a new SIM card and a new cellular service, and, though you will be using your old phone, you will not be subject to the long-distance and roaming fees of your old contract in your native country as long as you are using your new SIM card.
You must have an unlocked phone to do all this, because a locked phone will reject any SIM except for that designated by the manufacturer. To that purpose, there are businesses, online and in person, that will unlock a cellular phone for you. Also, you can buy unlocked cell phones - there are a great many available on the market.