The Goat Man is a man who lives in the Seam and owns a herd of goats. He is a filthy, impatient, old man. He has a hacking cough (from years in the mines), and his joints are swollen and twisted at irregular angles. He is lucky to have saved up enough to afford his goats. The Goat Man sells Lady to Katniss, a goat that she gives to Prim for her birthday.
The Goat Man never actually appears in the books, but he is mentioned several times. He speaks on page 271 in the first book. He is mentioned again in Catching Fire when Katniss comes home from hunting and the Peacekeepers are there. They ask where she has been and she tells them she was doing errands—which involved going to the Goat Man to ask him a question for Prim.