Why is it significant that Unferth is the person to hand Beowulf the famed sword Hrunting, with which he seeks to kill Grendel's mother?

This action signifies Unferth's respect for Beowulf. Earlier in the epic, Unferth challenges Beowulf's claims of heroism and attempts to discredit him. By giving Beowulf his sword.... he is publicly showing respect, and thus, in his own way, making an apology.