In the second stanza of the poem, Yeats alludes to the classical Greek myth of Leda and the swan. In this story, the Greek god Zeus took the form of a swan and, in that form, seduced and raped a princess named Leda. The child born of the rape was Helen of Troy, who has since become famous for her supposedly great beauty.
When the speaker says, in stanza 2, "I dream of a Ledaean body," he means that he dreams about great beauty. The "Ledaean body" is a reference to the beauty of Leda and also to the beauty of Helen, who was born of Leda. This classical allusion poses complicated ideas about beauty. Indeed, the Ledaean beauty of which the speaker dreams is a beauty born of violence. It is also a beauty, in the form of Helen, that supposedly sparked a war.
Also in the second stanza of the poem, Yeats uses symbolism when he references "a sinking fire." The fire here is symbolic of the speaker's life and passion, both of which are fading because the speaker is now an old man. The fact that the speaker says that the fire is "sinking" suggests that he has a keen sense of his own age. This image of the old man's diminishing life is in stark contrast, or juxtaposition, to the beauty of youth that the speaker sees in the school children. The speaker's age is emphasized in juxtaposition to the youth of the children, and the youth of the children, in turn, is emphasized by the age of the speaker.
In stanza 7 of the poem, the speaker says that images of youth are like holy relics and that both can "break hearts." This is an example of a metaphor. Yeats doesn't mean that images of youth can literally break hearts, but the metaphor emphasizes the idea that the beauty of youth can be painful. The beauty of youth is painful from the perspective of those who have lost it, and it is painful because it can only ever be temporary.