It is important to understand that Steinbeck doesn't give the character of Curley's Wife a first name. She is the catalyst in the story that begins the inciting incident.
We are given the information at the onset that George and Lennie had to leave Weed in a hurry because Lennie scared a woman by touching her too roughly. Once we meet Curley's wife, we know through foreshadowing that the events to come will involve her, because of her beauty and the way that she treats the two men. She likes George and he tells Lennie to stay away from her because she is trouble. Lennie tries to avoid her, but she is lonely and she wants someone to talk to her. When she finds Lennie alone in the barn, she is the catalyst that leads to the peak of the action of the story.
In addition, Curley's wife is another victim in the story. She is not accepted because the farmhands know that if Curley sees them talking to her, they will be fired. Curley wears a glove on one hand that he keeps soft for his wife, while on the other hand, he physically and mentally abuses her. She wants out because she doesn't like her husband, she thinks that he is a bad man. She unwittingly leads Lennie to his death.