After talking to Aventus you’ll learn that after his mother died (which I presume was the skeleton in the house) he went to live at the Honorhall Orphanage in Riften, where the headmistress, Grelod the Kind, treats the kids there like crap.

Head over to Riften and find Honorhall Orphanage. Go inside to scope out the place and you’ll meet Grelod (chances are she’s talking to all of the kids and it’s VERY clear that she’s scum and needs killing). In fact, instead of being sneaky you could kill her right here and now and all of the kids in the house will CHEER and thank you. There’s an adult in the house at times that will freak out, but this is one murder that will go un-reported. How crazy is that!?

Once you’re done, head back to Windhelm and talk to Aventus. He’ll thank you and will give you a family heirloom as payment (which isn’t worth very much) and this quest will be over. Read about the next quest to start it, since it doesn’t trigger right away…