What does it mean to hold a mortgage for a buyer?

It means that the seller becomes the lender. Instead of the seller receiving the full amount of the purchase price at the closing, the seller will receive monthly payments from the buyer. Those monthly payments will be the amount of the purchase price that wasn't paid at the closing, plus interest. If the buyer defaults in making the monthly payments then the seller has the right to foreclose.

Lisa is correct, you will be the bank and they will make payments to you every month. This can be achieved if your home is free and clear at the time of sale or you will have to payoff the first loan. Do a credit check on the buyers, ask for pay stubs and 1040's for the last 3 years. Do your homework before you do this also remember, if you do this they must get fire insurance and put your name on it as the first lien holder, so you will get paid in case of a fire etc.