An assumable mortgage is a home loan that a home seller can transfer to a potential buyer. The new buyer takes over the remaining mortgage payments, provided that they qualify for the assumption.
Assuming a mortgage may or may not make sense, depending on the interest rate and remaining balance of the loan. It doesn’t make sense when you can procure a lower interest rate with a new mortgage or when such a purchase would require more additional cash than a buyer can afford.
Most recent mortgages are not assumable, though FHA loans may be assumed.