(1) One in which the buyer agrees to fulfill the obligations of the existing loan agreement that the seller made with the lender. When assuming a mortgage, a buyer becomes personally liable for the payment of principal and interest. The original mortgagor should receive a written release from the liability when the buyer assumes the original mortgage.
(2) It’s exactly what you (likely) think it is: A home buyer takes on the existing mortgage taken out by the current homeowner/seller and pays off the remainder of the loan. This isn’t a terribly popular option for buyers — and, as a Trulia blog post points out, there are some restrictions with assumable mortgages — but it’s yet another avenue for buyers to take in their quest to purchase their first, next, or even dream home. Buyers who find it difficult to get a home loan with the desired terms are often ones who will assume a mortgage from sellers.