Final answer:
Beowulf wants Wiglaf to ensure that his heroic deeds are remembered, to lead their people, and to build a large burial mound in his memory.
Step-by-step explanation:
After Beowulf dies, he wants Wiglaf to do a few things, which further the heroic culture presented throughout the epic poem. Primarily, Beowulf wishes for Wiglaf to ensure that his story, his heroic deeds, and preferably his lineage continue to be remembered by the people. He trusts Wiglaf to become the new leader and take care of their people. More tangibly, Beowulf requests that a barrow, or a large burial mound, be built for him on the coast so that sailors can see it and remember him. The burial mound is meant to serve as a monument to Beowulf's life and achievements.