Beowulf wants the tall tower built at the edge of the water so that sailors can see it from a distance and remember his name. Thus Beowulf wishes to be remembered after his death. Also, as a man of the sea, he identifies with those who will come in their own journeys over the sea after his death. He wants the tower built so that "boats in the darkness / And mist, crossing the sea, will know it."
As recounted in "The Burning of Beowulf's Body," Beowulf's request is honored. The Geats build the tower "strong and tall," working on it for "ten long days." After Beowulf's monument is completed, the Geats seal his ashes within its walls and also bury the treasures won by Beowulf and Wiglaf. Once Beowulf's burial is complete, "twelve of the bravest Geats / Rode their horses around the tower, / Telling their sorrow . . . ."
In addition to the previous response, by burying the treasure within the tower a statement is being made about the cowardice of the men (besides Wiglaf) who flee rather than face the dragon. The king was expected to reward those who were loyal to him and, as Wiglaf points out to the men, their flight has disgraced them and their families. There will be no treasure to share. The tower becomes not only a monument to the greatness of Beowulf but also a reminder of the failure of his soldiers.
Remember too that to the people of this time, Fame is viewed as the thing most desired - the only thing that lasts beyond death. So this monument tower would also keep Beowulf's name and story in front of the people.