Yeats uses the first stanza to establish the elegiac tone of the poem--that is, this is a poem essentially about loss--and it is important to prepare the reader to understand the speaker's feeling, as he expresses it later in stanza three, that "All's changed. . . ." The poet, though, perceives the loss as bittersweet because he's confronted with such beauty at the outset of the poem.
"The Wild Swans at Coole" was written in 1917, the third year into World War I, a year after the Irish Uprising of 1916, two events that negatively affected Yeats' view of Irish society in particular, and the larger world in general. When Yeats uses Autumn as the season for this poem, we are meant to understand the season as symbolic of decline, a meaning that is confirmed later by Yeats's comment that "now my heart is sore."
Not only does the season help establish the tone of loss but also the time of day reinforces the tone: the poet is looking at the lake and swans not at the break of day but at twilight, yet another indication that time is not on the poet's side and that the subject of the poem might ultimately be about loss.
Despite the somber tone established by the details of Autumn and twiight, the poet, despite his "sore" heart, is still able to perceive the beauty before him--"autumn beauty," "Mirrors a still sky," "brimming water." All of these are beautiful and natural images and are the sweet part of his sense of loss.