The opening scene displays the tension between Robert and Catherine from the outset. The champagne he gives her isn't real champagne; she reminds him of a time that he opened a bottle in a bad way. They argue over her future. He warns her not to be lazy and waste her talent. When Hal comes and interrupts Catherine, the audience finds out that Robert wasn't really there. He died a week ago.
This sets up the plot and themes for the rest of the play. Catherine is worried that she's inherited her father's mental illness; she isn't sure she can trust herself. At the same time, she becomes upset later when Hal won't trust that she wrote the proof. Flashbacks reveal her relationship with her father, her relationship with Hal, and her authorship of the proof.
One of the themes of the play is uncertainty. Catherine can't be certain that she's completely sane, because of her illness that her father had. Moving from imagination to reality shows the audience that what she sees can't be completely trusted. Rather, it's possible that she can't know what's happening because she could have a mental illness. The switching between reality and her imagination helps illustrate this uncertainty from the outset.