The narrator of the poem "Ulysses" by Alfred, Lord Tennyson is Ulysses (Odysseus) himself. He has returned to his wife and son in Ithaca, and he rules the land as king. However, he is restless and longs once again for travel and adventure. He wants to give the affairs of the governing of the kingdom to his son, Telemachus, board his ship once again with his loyal mariners, and sail away into the unknown. He realizes that he is old and that death will put an end to all his deeds, and yet he feels that it is "not too late to seek a newer world." He proposes to "sail beyond the sunset" until he dies; in other words, they will head west.
According to mythology, Achilles was a mighty warrior who fought with Ulysses in the battle of Troy, as recounted in Homer's Iliad. Unlike Ulysses, Achilles did not survive the war. His mother, Thetis, had sought to make him invulnerable by dipping him in the River Styx, but the left heel, by which she held him, had not got wet. During the war, Paris, the son of the king and queen of Troy, shot a poisoned arrow into Achilles's heel and killed him. There are various versions of what became of Achilles after his death. According to some accounts, he ended up in the Elysian Fields, a sort of paradise where the deceased could be blessed and happy in the afterlife. Elysium also became known as the Isles of the Blessed or the Fortunate Isles, and their location was supposed to be in the western ocean at world's end.
In the poem, when Ulysses muses that perhaps he and his mariners might "see the great Achilles" at "the Happy Isles," he is suggesting that they might voyage far enough to find this paradise of the afterlife where Achilles went after he died.