Basically, a summary essay is an essay that addresses the main points of a much larger work in a much shorter work. This requires concise writing and an intricate understanding of the article about which the summary essay is being written.
In the most basic sense, a summary essay is written so that the reader gets the main points and ideas of a much larger work without investing the time to read the original work. It is important, in a summary essay, that you represent the points and general tone of the original article or text.