These are the roots left behind when the vine- most likely ivy - was torn/ripped down. They're very hard to remove because the glue they produce naturally to keep attached is very much unaffected by alot of things (soaps for instance).
Using a gas burner to taost them to a crisp and then some elbow grease (spatula/steel brush) will get the majority of it off. If the wall is still STAINED I'm afraid painting over it is the only option after that.
