In the story of King Arthur in Malory's Le Morte d'Arthur, how is Excalibur used as a symbolic element?
In Malory's Le Morte d'Arthur, Excalibur, the name of the sword young Arthur retrieves literally is a symbol of power among the leaders of the kingdom who are all vying for control upon the death of Uther Pendragon.
With Uther's death, the kingdom is in disarray with several of the barons struggling to gain control.
There are two popular versions of how Arthur receives Excalibur. In one, Arthur removes the sword that has been held fast in the stone, that no other man has been able to move; it is a sign to the barons that they have a new king.
In the other case, Merlin and Arthur ride up to the edge of a lake and...
...see an arm clothed in white samite, rising from the water and holding a sword.
(In this case, a young woman walks on the water to retrieve the sword and give it to Arthur.) The result is the same: Arthur becomes King. (This fulfills Uther's promise to Merlin that Arthur would one day take his father's place on the throne.)
Figuratively, in terms of what the sword will mean to Arthur and his life...
Excalibur is a symbol of the responsibility of power.
In "stories of old," there was a "moral" to the story, a lesson to be learned. We learn a quite a bit about great leaders based upon how they act, and whether they are aware of the lessons life has to teach them in their capacity as leader. We see Beowulf's bravery, generosity, and his humility to God in Beowulf. Grendel defies God, while Beowulf honors God. (The influence of Christianity on a story that is set in Sweden predates Christianity in the British Isles—where it is finally "recorded"—is evident.) In Shakespeare's Macbeth, Macbeth does not adhere to the lessons he has learned in service of King Duncan and Scotland. This leads to his downfall, and ultimately, his death.
In the epic poem by Tennyson, Idylls of the King, the reader learns that there is engraving on the sides of the sword's blade that speak of the temporal nature of kingship, but Merlin notes:
'Take thou and strike! the time to cast away / Is yet far-off.'
From the beginning, even as Arthur takes the sword, he knows that he cannot have it forever—just as he will not be king forever, or live forever.
With this knowledge, Arthur is charged to rule wisely, though his days as King will be numbered. The engraving may well be a reminder that one should not lose sight of his insignificance in the scheme of life. A king might believe he is above all others and responsible to none as long as he is king, but the words on the sword challenge him to avoid this mistake.
Excalibur gives Arthur power, but also reminds him of his responsibilities in his reign as king. He must be "wise and strong," as Arthur is when he first takes the throne. But he is unable to hold himself to the code he expects of others. His men owe their allegiance to God and King. He owes his allegiance to God, but when he realizes Lancelot (who he loves dearly) and Guinevere (who he loves slightly less) are committing adultery, he hesitates to act until forced to. Christian elements are present throughout the story: Arthur's failure to demand obedience from these two, and their allegiance to God, show his weakness as a king.
Arthur is not a great man like Beowulf; he is unable to remain dedicated to his responsibilities. He fails to see warning signs everywhere around him, which ultimately leads to his loss of wife, kingdom, sword, and life. The desire he has as a young man to protect England is lost to his human frailty.