Iris is everything that Memo's not. She's mature, sympathetic, supportive, and she wants Roy to just be himself. He meets her in a grassy park and takes her swimming in a lake. Memo's more comfortable in cars and hotel rooms. Roy's totally relaxed with her; around Memo, he's in a constant state of agitation.
She just shows up one day to help Roy break his slump, but she's not totally unannounced. A fortune-teller named Lola told Roy that he would fall in love with a dark-haired lady. He was expecting some news about Memo, who's redheaded, so when he meets the dark-haired Iris we have to think that this is who Lola was talking about. When she appears at the game, it's like she has some kind of magical power:
He caught the red dress and a white rose, turned away, then came quickly back for another take, drawn by the feeling that her smile was for him. Now why would she do that for? She seemed to want to say something, and then it flashed on him the reason she was standing was to show her confidence in him. At the same time he became aware that the night had spread out in all directions and was filled with an unbelievable fragrance. (6.128)
It's as if she's sent to rescue Roy. Roy tells Iris that her showing up at the game broke the spell that had put him into a batting slump.
"Why'd you come—the first time?"
[…] "Because I hate to see a hero fail. There are so few of them." (7.42)
Her unbelievable fragrance might be sexual attraction or just joy, but either way we know Iris is a force for good. She goes on a date with Roy without playing any games with him like Memo does, and is all around a cool lady. That is, until she reveals her secret: she has a grown daughter. That doesn't seem to bug Roy too much, so she reveals another secret: her daughter has a baby, which makes Iris a grandmother. That does bug Roy. He thinks it would make him feel to old to have a relationship with a grandma.
Iris really doesn't appear until 2/3 the way through the novel, but she's an important counterpoint to Memo's wicked ways. Her love for him is constant, even though he more or less ignores her after their first meeting. She seems to be a responsible adult whose values are in the right place. She encourages Roy to be the hero he can be:
"Without heroes, we're all plain people and don't know how far we can go. […] Yes, it's their function to be the best and for the rest of us to understand what they represent and guide ourselves accordingly." (7.44-7.46)
Iris is a "real person." She's lived in the real world and done okay. Roy senses this:
[…] Memo was remote, even unreal. Strange how quick he forgot what she was like, though he couldn't what she looked like. Yet with that thought even her image went up in smoke. Iris, a stranger, had done for him what the other wouldn't, in public view what's more. (7.17)
Roy finds Iris attentive and comforting, and he does what he's never one before—tells her about what happened with Harriet Bird. He shares his deepest pain:
She stroked his brow slowly with her fingers.
What happened fifteen years ago, Roy?
Roy felt like crying, but he told her—the first one he ever had. "I was just a kid and I got shot by this batty dame on the night before my tryout and after that I just couldn't get started again, I lost my confidence and everything I did flopped.
He said this was the shame in his life, that his fate, somehow, had always been the same (on the train going nowhere)—defeat in the sight of his goal. (7.96-7.99)
Roy tells her that he's attracted the wrong type of woman, but Iris is different:
He laughed harshly. "I sure met some honeys in my time. They burned me good."
"Why do you pick that type?"
"It's like I say—they picked me. It's the breaks."
You could say no, couldn't you?"
Not to that type of dame I always fell for—they weren't like you." (7.103-107)
Iris is sympathetic to Roy's suffering. In fact, she suggests that it happened because he was too good a person. And she gives him this pearl of wisdom that made it verbatim into the movie version, so it must be important:
"We have two lives, Roy. The life we learn with and the life we live with after that." (7.126)
Roy's revelation makes her share her own, that she made a "mistake" when she was young and ended up having a daughter. Then more revelations: that daughter had a daughter. Even though Iris accepts Roy's sad past, he can't accept hers. He decides that he can't be with her, but that doesn't stop him from having sex with her.
At the last game of the season, where Roy's agreed to fix the game, he drills a hard foul ball right into Iris. She barely manages to tell him that she's pregnant with his son before she gets carried off to the hospital. Is this scene meant to represent Roy's attack on goodness in general as he's about to sell out? It seems to have a huge effect on him. When he goes back to finish his at-bat, Malamud tells us that the pitcher "saw a different man" (10.30).