Why does Mrs. Gibbs change her mind in Our Town? This refers to a speech in which Mrs. Gibbs summarizes her objections to George's marriage that is compared to one in which she accepts the idea.
Mrs. Gibbs is a character who, when she first hears about George's plans to marry Emily, reacts in a way that perhaps is understandable given her love for George and her concern for him. Note what she says in the following speech:
I declare I don't know how he'll get along. I've arranged his clothes and seen to it he's put warm things on--Frank! They're too young. Emily won't think of such things. He'll catch his death of cold within a week...
Her objections in this speech are based on her maternal concern for George and her worry that he will not be looked after properly. However, after a little time to think about it, she accepts that she needs to let go and that they need to marry:
And once he's on the farm, he might just as well have a companion, seeing he's found a fine girl like Emily... People are meant to live two by two in this world... Yes, Frank, go up and tell them it's all right.
Mrs. Gibbs seems to have moved in this speech from shock to acceptance. Having had time to think about it, she begins to see that George is growing up and that it would be good for him to have a wife as he starts the next chapter of his life. Mrs. Gibbs therefore changes her mind as she begins to think about her son's marriage and has time to let the shock subside.