Let's approach the answer in two parts--the reader-response component and the story itself.
The essence of the reader-response is the individual reader's response to a text. That is, every reader approaches a literary text with a different "agenda" based on that reader's interests, life experience, familiarity with analyzing literature. In other words, almost every reader-response criticism of a particular text is going to be slightly different simply because every reader brings something unique to the experience. One of the important element of reader-response criticism is that one's response, uniess it's completely bizarre and uninformed, is neither right nor wrong--it is one person's response to a text, and individuality is an important factor.
Now, chances are that your instructor expect some level of common response among the students--an understanding of the underlying themes in the story, the plot, who the narrator is and what kind of narrator you have. In the case of "A Clean, Well-Lighted Place," you may respond to the importance of the setting: why is a clean, well-lighted place important to one or more of the characters? You might also respond to the attitude of the older characters in the story, whose focus seems to be on how and where they spend their remaining time. For example, both the old patron and the old waiter feel that their time in life is drawing to an end, and their choice of where and how to spend that time is important to them. That theme may have attracted your interest.
Another theme Hemingway explores is the different ways that the young and old look at their lives, and that may be an element that interests you based on your own experience as a young person.
In essence, the instructor is most likely looking for your unique perspective on one or more of the themes in the story, and because it's your perspective, it will be slightly different from other students' perspectives. You may all discuss the same theme but in slightly different ways based on each person's experience and understanding of life. That's why the assignment is called a "reader-response."