Kate is Joe Keller's wife and Chris Keller's mom. Arthur Miller refers to her as "Mother," in the script. Her motherliness is one of her defining characteristics, as Miller stresses in the stage directions preceding her first entrance:
Mother […] is in her early fifties, a woman of uncontrolled inspirations, and an overwhelming capacity for love. (1.230)
Kate's love is accompanied by a need for control. When she senses that Chris is falling for Ann (which Kate disapproves of), she drops several unflattering hints about Ann's appearance: "I think her nose got longer" (1.256) and "You gained a little weight, didn't you, darling?" (1.334).
She also wields her love as a weapon. Just as Joe laughs and jokes to dispel tension, Kate nurtures to manipulate. When George arrives in Act 2, a threat to she and Joe's security, Kate spins a web of comfort around him that almost makes him forget his desire for justice.
Like Joe was just saying – you move back here, he'll help you get set, and I'll find you a girl and put a smile on your face. (2.378)
She even remembers his shirt size. Before she slips up about Joe never being sick, she almost sucked him in.
Miller describes Joe as kind of a dolt, but Kate is not. She's the clever and wily one; she understands much more quickly the repercussions of things. The stage directions are full of references to her sharp instincts. When Chris talks about Ann, Mother listens "with an undercurrent of observation" and subtly undermines his budding love (1.260). At the end of Act 1, dreading the arrival of George, "Mother sits in a chair downstage, stiffly, staring, seeing" (1.623). She's planning how to handle him. It's up to Kate to strategize, which she has the capacity to do even as everything is blowing up in her face. Joe recognizes her power. When Chris finds out about his father's guilt, Joe begs her, "Tell me, talk to me, what do I do?" (3.49).
Kate is intelligent, but she's by no means totally objective or rational. Since the disappearance of her son, she's looked increasingly to religion, dreams, signs, and even horoscopes to make sense of reality. When Larry's tree is struck by lightning, she tells her husband, "Laugh, but there are meanings in such things. She goes to sleep in his room and his memorial breaks in pieces" (1.303). And of course there's the matter of commissioning Larry's horoscope from Frank. Kate's superstition is a defense against her husband's guilt – and her own. She explains her philosophy to Ann:
"Certain things have to be, and certain thing can never be… That's why there's God, so certain things can never happen." (1.410).
Kate is purposely vague, but what she means is what she says later, explicitly: "God does not let a son be killed by his father" (2.519).