Every SIM Card has unique serial number called ICCID - Integrated Circuit Card Identifier. It's stored in SIM Card memory or printed on the card itself.
Serial number might be required in different cases. It can be used for verification. Your carrier might ask you to provide this number when you are registering phone or changing a phone number. The operator can also track the location of the phone base on SIM Card serial number. If you want to move your phone number from one operator to another SIM Card serial number is required.
Unique number should be engraved or printed on the SIM Card. You have to open your phone and get SIM Card from it. The serial number should be on the card and it's 19 or 20 digits long.
You can also get a SIM serial number without opening the phone. Select your system and check how to get the SIM serial number.