A mortgage is putting a property as a guarantee to a lender as a security for a mortgage loan.
While a mortgage in itself is not a liability or a dept, it is evidence of a debt. It is a transfer of an interest in property, from the owner to the mortgage lender, on the condition that this interest will be returned to the owner of the property when the terms of the mortgage have been satisfied or concluded.
In other words, the mortgage is a guarantee for the loan that the lender makes to the borrower. In all but a very few states, a mortgage creates a lien on the title to the mortgaged property.