When someone borrows against a piece of Real Property using a Mortgage, they (the borrower) maintain Title to the property, and the Mortgage is a Lien on that property.
When someone borrows against Real Property using a Deed of Trust, the property is deeded to a neutral third party called a Trustee. This Trustee holds title to the property, and distributes title to the property under the terms of the Deed of Trust. If the borrower (called the Trustor) pays off the loan, title is given to the borrower. If the borrower fails to pay as agreed, the Trustee has the power to hold a public auction, and sell the property for the benefit of the lender (called the beneficiary). Just as with the Mortgage, the funds from the sale would go first to paying off the beneficiary (lender) and anything above that would go to the borrower, if there are no junior lien holders (2nd mortgage, ect.).
To foreclose on a mortgage takes 6 months and thousands of dollars, where as a Deed of Trust takes 3 months and an attorney.