The "thing" spoken about in this passage is connection with...
The last sentence of the story "Sophistication" reads,
"Man or boy, woman or girl, they had for a moment taken hold of the thing that makes the mature life of men and women in the modern world possible."
The "thing" spoken about in this passage is connection with another human being. The central theme in Winesburg, Ohio, from which the story is taken, is the inability of human beings to make true connections with other people. Because of this, they become what Anderson calls "grotesques," individuals stunted in emotional growth and doomed to live in isolation. In "Sophistication," George Willard is about to leave Winesburg, but his leaving is bittersweet;
"To his mind his new sense of maturity set him apart...he wanted someone to understand the feeling that had taken possession of him...with all his heart he wants to come close to some other human, touch someone with his hands, be touched by the hand of another..., he wants, most of all, understanding."
George turns to Helen in hope that, because she is a woman, she will be able to give him that understanding. It is true that he is attracted to her, but it is not attraction of a physical nature that he seeks. George thinks,
"He wanted to love and to be loved by her, but he did not want at the moment to be confused by her womanhood."
George wants something deeper, a communion of souls that transcends the physical, and fortunately, Helen wants the same thing -
"In the mind of each was the same thought. 'I have come to this lonely place and here is this other,' was the substance of the thing felt."
George and Helen kiss for awhile, but it is not in physical joining that they will find fulfillment now. They play like children, to relieve their embarrassment, and then they have a period where Helen takes George's arm and walks beside him "in dignified silence;"
"For some reason they could not have explained they had both got from their silent evening together the thing needed."
George and Helen have connected, in complete honesty of heart and purity of soul. They have achieved something that is almost impossible for individuals to do, hindered as they are by their own obsessions. Maturity cannot be truly realized without someone to share it with, even if just for a moment. It is not romance, but a spiritual connection with another human being that makes it possible for George to enter adulthood with authentic maturity.