The conclusion is the second most important part of your essay, after the introduction. Just as the introduction had the primary purpose of drawing the reader in, the conclusion's foremost function should be to leave the reader with a lasting impression. This section will offer guidelines on how to maximize the impact of that impression. These guidelines can be grouped into three categories, each of which encompasses a lesson of what not to do.
The chief difference between these two tactics is that the former deals with themes while the latter deals with facts/experiences, though there is some overlap. You do not need to recap the essay paragraph-by-paragraph. You do not need to remind the reader of the experiences you discussed (except as individual experiences might be tied to certain themes you want to synthesize).
You do want to reiterate key themes, but preferably not in a way that merely repeats them. Ideally, the process of synthesizing them will add a fresh perspective. Try to tie themes together and demonstrate how they complement each other. Of course, you should stay away here as always from trite and clichéd generalizations.
This applicant spends the bulk of his essay describing his compassion and the work he did after not being accepted to medical school the last time he applied. As the essay progresses, he shows how his current work has made him more conscious of his desire for personal interaction. Thus the intersection of his two topics grows apparent, and in his last sentence he offers the following synthesis: "I know that this process of maturing will make me a better and more compassionate doctor, and I now feel more prepared than ever for the rigors of medical school." He does not overstate his case but makes a natural connection between maturity and compassion. The point is both coherent and, at this stage of the essay, fresh - the two elements that make for a lasting impression.
If in the process of synthesizing you can invoke your introduction, that will add a strong sense of closure. There are a number of different ways this could be accomplished. You might complete a story you started in the introduction, or you might show how something has changed in your present since the timeframe of the introduction.
One way to ensure that your last paragraph has something fresh to say is to tie your ideas to some broader implications, whether about yourself or your field. But don't get carried away: some applicants think they have to make reference to saving the world or derive some grand philosophical truths from their experiences. Stay grounded and focused on your personal details.
This applicant brings up a problem with the health care system in his second paragraph. Thus his conclusion relates this issue to a greater principle: "As a doctor, I hope to participate in these changes in order to benefit more people than are currently being served. Doctors should be able to serve people of all different races, ages, backgrounds, and cultures. I intend to use my skills and unique experiences to achieve this vision of what I think a doctor should be." Again, appealing to outside principles is only one way to speak to broader significance. You could achieve similar results by relating your experiences in medicine to general trends in your life. The point is not to reach as far as possible, but rather to fulfill that primary purpose of leaving a lasting impression by having something fresh to say at the end.
We have used the word "fresh" several times here, and we're thinking mainly of perspectives and ideas. You should avoid adding entirely new information about your experiences. In shorter essays, you might have to pack details in everywhere, but in general, if it's an important experience, it should come earlier.
That said, speaking of goals in your conclusion is a strong way to end. Some essays will be chiefly about the writers' qualifications and intentions, but they won't touch on specific goals until all of that has been established. The delineation of goals can be like a process of synthesizing, because you are trying to tie your themes together in the context of where you will go next.
This applicant enumerates specific goals in his last paragraph: what position he hopes to obtain, what he will specialize in, and where he will work. The essay clearly has been building up to this point, and so the conclusion is fitting.
You may also want to make reference to the specific schools to which you are applying (some questions will ask why you want to attend). This information can come earlier, but it's not unacceptable to bring it up in the conclusion.