This item is just what it sounds like: Someone Else's Family Portrait! It costs 10 coins and it has no special abilites, aside from being warped when scorched/burned. After you burn your house down, the family in the portrait can be seen outside, singing as the choir in the background music.
It is part of the "Someone Else's" set, alongside Someone Else's Credit Card.
"The more you look at it, the more they look familiar."
This might mean this is actually a portrait of the player's family.