Mobile Station
The mobile station (MS) consists of the mobile equipment (the terminal) and a smart card called the Subscriber Identity Module (SIM). The SIM provides personal mobility, so that the user can have access to subscribed services irrespective of a specific terminal. By inserting the SIM card into another GSM terminal, the user is able to receive calls at that terminal, make calls from that terminal, and receive other subscribed services.
The mobile equipment is uniquely identified by the International Mobile Equipment Identity (IMEI). The SIM card contains the International Mobile Subscriber Identity (IMSI) used to identify the subscriber to the system, a secret key for authentication, and other information. The IMEI and the IMSI are independent, thereby allowing personal mobility. The SIM card may be protected against unauthorized use by a password or personal identity number.
GSM phones use SIM cards, or Subscriber information or identity modules. Memory modules. They're the biggest difference a user sees between a GSM phone or handset and a conventional cellular telephone. With the SIM card and its memory the GSM handset is a smart phone, doing many things a conventional cellular telephone cannot. Like keeping a built in phone book or allowing different ringtones to be downloaded and then stored. Conventional cellular telephones either lack the features GSM phones have built in, or they must rely on resources from the cellular system itself to provide them. Let me make another, important point.
With a SIM card your account can be shared from mobile to mobile, at least in theory. Want to try out your neighbor's brand new mobile? You should be able to put your SIM card into that GSM handset and have it work. The GSM network cares only that a valid account exists, not that you are using a different device. You get billed, not the neighbor who loaned you the phone.
This flexibility is completely different than AMPS technology, which enables one device per account. No swtiching around. Conventional cellular telephones have their electronic serial number burned into a chipset which is permanently attached to the phone. No way to change out that chipset or trade with another phone. SIM card technology, by comparison, is meant to make sharing phones and other GSM devices quick and easy.

On the left above: Front of a Pacific Bell GSM phone. In the middle above: Same phone, showing the back. The SIM card is the white plastic square. It fits into the grey colored holder next to it. On the right above. A new and different idea, a holder for two SIM cards, allowing one phone to access either of two wireless carriers. Provided you have an account with both. :-) The Sim card is to the left of the body.