You will want to focus on the conversation that Leila has with the old man who dances with her and suddenly bursts her bubble of illusion. Note the picture of old age that is painted by Leila's unpleasant partner of the future she can expect to have:
"And you'll smile away like the poor old dears up there, and point to your daughter, and tell the elderly lady next to you how some dreadful man tried to kiss her at the club ball. And your heart will ache, ache," the fat man squeezed her closer still, as if he really was sorry for that poor heart, "because no one wants to kiss you now."
The irony is obvious. In Leila's very first ball, where it becomes quite clear that she is the belle of the ball, she is confronted with the future that awaits her. However, in spite of this unpleasant reminder of her fate, Leila finds that quickly youth triumphs over old age, for now, as she forgets the old man's words and even the old man himself as she starts dancing again, and her feet "glided, glided" with the excitement of the vision of everything becoming "one beautiful flying wheel."
In her first ball, Leila is first introduced to the world of a ball. She's an innocent girl from the countryside and wasn't really exposed to any of this. And when she is, excitment fills her. From what people are wearing to the thought of dancing with young men and in the midst of all this comes an old fat grumpy man. And so in the middle of all the young men and women comes and aged fat man. This fat man tells Leila who is still in her youth about what her future might be like. She'll be an old lady trying to talk about the horrible men that try to kiss her daughter and how no one kisses her. This shows that when Leila is just begining to see the world and see the magic of youth, she's slapped with reality and what might be the end of her happy feeling inside. But then again the power of youth empowers her and she has already forgotten the horrible words of the fat man.