Barliman was the owner of the Prancing Pony inn in Bree. He was a Man, but as Bree was inhabited by both Men and hobbits, he had two hobbit employees: Bob, who worked in the stables, and Nob, a servant.
Warning: Wikipedia contains spoilers
He had a notoriously bad memory; for example, he forgot to tell Frodo that Gandalf had left a letter for him, leaving Frodo uncertain as to Gandalf's fate. In The Return of the King, Barliman was amazed to learn that Strider, a former patron of the Prancing Pony, had become king of Gondor.
In Peter Jackson's movie The Fellowship of the Ring, he is played by David Weatherly although the character is not named and most of his scenes from the book (including the reference to Gandalf's letter) are not in the film.