A non-recourse mortgage is a mortgage that has gets special treatment in foreclosure. With most loans that are foreclosed upon the amount of the loan that was not paid off when the foreclosed property was sold is still owed by the borrower.
In Foreclosure a Non-Recourse loan is fully satisfied when the real estate behind the loan is foreclosed upon. If you owe $300,000 on a house that is foreclosed upon and the bank sale only nets $200,000 the bank cannot come after you for the extra $100,000. In a Recourse loan you would still ow the $100,000.