Gawley's Horn is an object left for The Heir by his ancestors in a secret cave behind his house. It enables breaking open the seals of Sendell, thus leading to new places. To use the horn, the person should blow it towards a Seal of Sendell.
Twinsen finds the Horn of Gawley, along with Sendell's Medallion, in a locked room in the cave behind his house, to which he can enter after retrieving LeBorgne's key from the Maritime Museum. He can use the horn right after finding it, on a Sendell's Seal in the room, which reveals a clover leaf.
Even though behind most seals there are only bonuses like clover leaves, some seals are necessary for Twinsen to go through. For example, he has to use the horn on the Sendell's Seal in the White Leaf Desert, so that he can meet Joe the Elf and get the Elves Club card from him. Another example is near one of the Runic Stones in Proxima Island, where Twinsen has to blow the horn so that he can get to the stone.
Twinsen also needs the horn to break into the Teleportation Center on Brundle Island and to find the third runic stone in FunFrock's Secret Fortress. A Sendell's Seal is also blocking the way down to Sendell's Well.