Bamfurlong was a farm in the boggy region of the Marish in the eastern Shire. It was the home of Farmer Maggot, who (like the other Hobbits in this inhospitable area) lived above ground rather than in a traditional Hobbit-hole. Maggot's farm was well-known in the area for his mushrooms, which he protected fiercely against trespassers with his three fearsome dogs.
The name Bamfurlong is an old English one. Tolkien suggests that it comes originally from words meaning very roughly 'bean-field', though definite knowledge of its meaning is now lost.