IMSI = International Mobile Subscriber Identity. This is a unique identifier that defines a subscriber in the wireless world, including the country and mobile network to which the subscriber belongs. It has the format MCC-MNC-MSIN. MCC = Mobile Country Code (e.g. 310 for USA); MNC = Mobile Network Code (e.g. 410 for AT&T), MSIN = sequential serial number. All signaling and messaging in GSM and UMTS networks uses the IMSI as the primary identifier of a subscriber.
The IMSI is one of the pieces of information stored on a SIM card.
ICCID = Integrated Circuit Card ID. This is the identifier of the actual SIM card itself - i.e. an identifier for the SIM chip. It is possible to change the information contained on a SIM (including the IMSI), but the identify of the SIM itself remains the same.