"SSN" or "Social Security Number" is a nine digit number that is issued by the federal government. This number is used to track Social Security savings but is also used by creditors, banks, employers, hospitals and other organizations.
A "personal guarantee" is contract whereby an individual or entity takes responsibility for payment of debt or performance of some obligation of a third party if that third party fails to perform. For example, banks will sometimes require personal guarantees for loans made to credit risky borrowers.