The passage refers to the storm of emotions Laura feels as the result of what has just happened to her in her meeting with Jim O'Connor. Jim kisses her, leaving her with "a bright, dazed look." Laura is at first bewildered, then she smiles. She does not hear what he says immediately following the kiss; she is still living the moment.
In Jim's rambling speech that follows, Laura begins to realize the truth. Jim won't be calling again because he is engaged to another girl. Completely oblivious to the cruelty he is inflicting, Jim tells Laura about his intended, and then explains to her--quite ironically--the power of love. It is at this point in Jim's excruciatingly painful remarks that Tennessee Williams indicates in his stage directions the effect of Jim's words on Laura:
Leaning stiffly forward, clutching the arm of the sofa, Laura struggles visibly with her storm. But Jim is oblivious, she is a long way off.
During her evening with Jim, Laura had dared to leave the emotional safety of her own world. She had begun to feel and perhaps to dream an old dream of Jim. When reality intruded, Laura was overwhelmed with a new and sudden sense of loss.