Pipe mud is a mixture of cigar ash and water (or sometimes honey) which is put into a spot in the chamber that's beginning to burn out. It's allowed to dry for a while, and then it's smoked over so it will harden an protect the spot, preventing it from burning all the way through.
When I've done this, I just apply it to the burnt spot without removing any of the material. The rough surface gives the mud more of a purchase to grab onto, and stays in the area well.
Russ