Sister Irma is Jean's fantasy crush, but he never meets her. She's taking art classes not because she wants to be a great artist, but because she'll be teaching art to kids at the convent and wants to be a better teacher. We don't know what she looks like, because she enclosed a photo of her convent, instead of the requested photo of herself with her art school application. Though Jean pictures her as a woman about his age, her age is unknown because she doesn't answer the age question on the art school questionnaire. According to Jean, she's a fabulous artist, or at least has the potential to be one. And that's about all we know for sure.
Considering how important she is to the story, her character is remarkably thin. We can't know her any more about her than Jean knows. In fact, we can't even know if she read Jean's letter to her, or how she felt about it. Though, Father Zimmerman has withdrawn permission for her to attend art school, as Jean learns via a letter from the Mother Superior, we don't know if Sister Irma is pleased or displeased by the situation.
Like Jean's mother, and even Bobby, Sister Irma is important because she is absent, out of reach, unattainable, and unapproachable. She also contrasts Jean in that she, presumably, values religion over art. (For Jean, art is a kind religion.) By letting Sister Irma go at the end of the novel, Jean could be acknowledging that each person has his or her own way of living, and that it is not his responsibility to influence those who choose differently than he does. If you are interested in Sister Irma you should definitely check out "What's Up With the Ending?"