Taken from the Wikipedia page, the International Mobile Station Equipment Identity (IMEI) is a number, usually unique, to identify 3GPP (i.e., GSM, UMTS and LTE) and iDEN mobile phones, as well as some satellite phones. It is usually found printed inside the battery compartment of the phone, but can also be displayed on-screen on most phones by entering *#06# on the dialpad, or on an iPhone by going to Settings / General / About.

You can use your IMEI number to perform an iCloud unlock on your IMEI number if your iPhone somehow becomes locked with iCloud. You can also check to see if your IMEI number has been reported lost or stolen here and here.

Generally speaking, if your phone is lost or stolen, you can call your carrier with the IMEI number and tell them to blacklist the phone. The carrier will blacklist the phone for that carrier, but also may blacklist the phone for ALL carriers.