Usually refers to a fixed rate mortgage where the interest rate is "bought down" for a temporary period, usually one to three years. After that time and for the remainder of the term, the borrower's payment is calculated at the note rate. In order to buy down the initial rate for the temporary payment, a lump sum is paid and held in an account used to supplement the borrower's monthly payment. These funds usually come from the seller (or some other source) as a financial incentive to induce someone to buy their property.
A "lender funded buydown" is when the lender pays the initial lump sum. They can accomplish this because the note rate on the loan (after the buydown adjustments) will be higher than the current market rate. One reason for doing this is because the borrower may get to "qualify" at the start rate and can qualify for a higher loan amount. Another reason is that a borrower may expect his earnings to go up substantially in the near future, but wants a lower payment right now.