In the poem "Morte D'Arthur" by Tennyson, Sir Bedivere had been mourning the loss of the old way of life of the Knights of the Round Table as he was saying that "the true old times are dead" and that the "whole Round Table is dissolved." As the wounded Arthur prepares to sail for the legendary Avilion, he attempts to give Bedivere some comfort or at least courage by agreeing that, yes, his Knights and the Round Table were done but that it was just the changing of the tides of time as the old moves out to make way for the new.

From Arthur's perspective, the "old order" was his kingdom and the ideology that he had established that his Knights had lived by. So he says the "old order changeth" and means that order--the governance, the established way of things--represented by himself and his Knights was over, was gone, was changed and that something new would now arise to fill the gap, the empty space left by the dissolution of the Round Table.