A mortgage is granting of a lien on real property, such as a home, by a debtor (borrower) to his creditor (lender), such that the property is security for the repayment on a loan. Once the loan is paid, the mortgage should be discharged.
Hypothecation refers to the right that a creditor has to liquidate goods, securities, or other assets, if you fail to service a loan.
A sub-prime mortgage is one where the borrower has a demonstrated inability to abide by the terms of a credit obligation.