Holding a mortgage means that, instead of selling a house to a seller who has gotten a loan from the bank, you instead arrange to receive monthly payments from them directly until the house is paid off. There are a few different sides to this technique.
First off, this appears as undesirable to many people because instead of receiving a large lump sum right away, they get monthly payments over time. But then again, if you get payments instead of a large sum, you also get to earn interest. This interest would be a better return than what you would get putting the money into a savings account, so for this reason, some people like the idea of holding a mortgage.
Holding a mortgage is definitely a risk. If the buyer falls behind on the payments, then you can always foreclose and resell the house. However, you run the risk then of the occupants trashing the house. If you need to make costly repairs, you will spend money on that. Also, remember that money value changes, so the money that you would make in one large lump sum might be better invested than money gained over time.
Most of what causes people to decide on holding a mortgage lies with the situation, and whether or not they need, or want, a large lump sum of money up front. It is also pretty common to see a relation hold a mortgage if selling property to a family member.