Traditional academic essays are pieces of writing which are designed to demonstrate the following points:
This means that you have to combine important ideas, examples, and interpretations from other writers with your own. All of these have to be put together in a linear, written format (making one point, then moving on to the next), which persuades the reader that your line of argument is a convincing one.
Take a look at this great page developed by The Library, Technological University of the Shannon: Midwest. Click on the What is an Essay to access this page.