Butterbur is the innkeeper of The Prancing Pony in the town of Bree, on the other side of the Old Forest. We know from the Prologue that The Prancing Pony has been in the Butterbur family for generations, and that they are well-known for growing pipe-weed. The Prancing Pony is a central meeting place for Bree's residents, so Butterbur is an important person in the village.
He's also a friendly, helpful, but not-overly-bright guy. When he sees the four Hobbits, he remembers something, but he can't recall what it is, exactly. This thing that slips the busy innkeeper's mind is a letter from Gandalf, which the Wizard left for Frodo three months before Frodo arrived at The Prancing Pony. The letter tells Frodo to leave the Shire early, and to look for a man called Strider/Aragorn for help. Sadly, Butterbur forgot to mail this letter, leading to Frodo's departure from the Shire as planned in late September.
As one of the only characters in all three books who is not actively involved in the War of the Ring, Butterbur becomes Tolkien’s go-to reference for sheltered, ordinary folk who need to be protected from Sauron. Aragorn later comments, "'Strider' I am to one fat man who lives within a day's march of foes that would freeze his heart, or lay his little town in ruin, if he were not guarded ceaselessly" (2.2.68). That fat man is Butterbur, and Aragorn is glad to keep him safe and ignorant of the danger he runs just living in Middle-earth in these dark days.
Butterbur is also a deeply honest man: when he discovers that the Black Riders have broken into The Prancing Pony and tried to kill Frodo and the Hobbits in their sleep, he gets really upset. And when Bill Ferny horribly overcharges Frodo for a pony to replace the ones that ran away from the riders, Butterbur pays for the animal himself. He also gives Merry another eighteen pence for compensation for the five lost ponies. As Gandalf comments later, Butterbur has plenty of sense – he may not be the brightest of bulbs, but he's excellent at managing his business in his own world of The Prancing Pony.