The IMEI number is used by a GSM network to identify valid devices and therefore can be used for stopping a stolen phone from accessing that network. For example, if a mobile phone is stolen, the owner can call his or her network provider and instruct them to "blacklist" the phone using its IMEI number. This renders the phone useless on that network and sometimes other networks too, whether or not the phone's SIM is changed.
The IMEI is only used for identifying the device and has no permanent or semi-permanent relation to the subscriber. Instead, the subscriber is identified by transmission of an IMSI number, which is stored on a SIM card that can (in theory) be transferred to any handset. However, many network and security features are enabled by knowing the current device being used by a subscriber.