A slum is where the value of houses or land in a certain neighborhood drops so low that the only people who wish to live there are the extremely poor.
How does the value of an area drop? Simply because less people want to live there. This can be for all sorts of reasons. Perhaps there are no decent jobs to be had nearby? Perhaps new industrial areas are beginning to develop across the road and unsightly factories spring up. (Think Sim City!)
Everyone will want to leave to live in a nicer area, so the demand for the houses will drop. Whoever owns the houses now will have to ask for lower prices or no one will buy the land off them. Prices can get so low that the extremely poor can afford to purchase the house.
The wealthy move out, the poor move in.