The Hornblower Family was an old and important family of the Shire's Southfarthing. Its most famous member was Tobold Hornblower of Longbottom, who introduced pipe-weed into the Shire, and his family remained associated with industry. Their Longbottom Leaf variety was famous, and indeed barrels of Leaf bearing the Hornblower mark were found as far afield the ruins of Isengard.
From Tobold's time, and perhaps earlier, the Hornblowers were one of the Shire's more important families. The importance of the family is also seen in the jewel-name of Amethyst, and her marriage into the Bolger Family. Frodo Baggins himself had Hornblower blood — his great-grandfather Largo Baggins married one Tanta Hornblower.
The meaning of this old family name is occupational; perhaps one of Tobold's ancestors, or himself, actually did blow a horn of some kind. Perhaps the name is a punning reference to pipe-smoking.
Hornblow and Hornblower are real-life English surnames.