A loan that is secured with a pledge of collateral, but for which the borrower is not personally liable. In the event of default, the lender's recovery is limited to the collateral and nothing else.
Examples are auto loans and mortgages (depending upon the particular laws).
Central banks can also engage in this. In the case of Federal Reserve, emergency lending facilities can extend nonrecourse loans.
A loan loses its nonrecourse status if a borrower breaches the loan agreement, for example, by misrepresenting its eligibility for a loan.