Wild swans are referred to both in the story the minister tells Rose when he first engages her in conversation, and then they are used as a metaphor for her orgasm, as what Rose sees through the window of the train in nature corresponds with what is happening to her physically. Note how Munro achieves this in the following quotation:
The gates and towers of the Exhibition Grounds came into view, the painted domes and pillars floated marvellously against her eyelids' rosy sky. Then flew apart in celebration. You could have had such a flock of birds, wild swans even, wakened under one big dome together, exploding from it, taking to the sky.
The use of the word "exploding" clearly refers to the physical and sexul sensation that Rose herself is experiencing, and the symbol of the wild swan becomes a very appropriate symbol of sensuality and nature that is used to indicate the way that what Rose sees through the train window comes to define her feelings and what she experiences. Whether Rose actually imagined this event or whether it was her own fantasy is deliberately left ambiguous, but the title draws attention to the way that we are presented with a young woman who has her first sensual experience and comes to take her first flight as a woman.