The Grubb Family was an important and wealthy family of the Shire-hobbits. At least some of the family were involved in auctioneering, a fact we can deduce from the name of the company set to sell Bilbo Baggins's belongings: Grubb, Grubb and Burrowes. In fact, Bilbo had a slight connection with the family: his paternal grandmother was Laura Grubb. She married Mungo Baggins, and together they produced five children, of whom the eldest was Bungo Baggins, Bilbo's father.
The name is meant to recall the English verb grub "dig, root, in the ground".