In the literary essay, you are exploring the meaning and construction of a piece of literature. This task is more complicated than reviewing, though the two are similarly evaluative. In a review you are discussing the overall effect and validity of written work, while in a literary essay you are paying more attention to specifics.
A literary essay focusses on such elements as structure, character, theme, style, tone, and subtext. You are taking a piece of writing and trying to discover how and why it is put together the way it is. You must adopt a viewpoint on the work in question and show how the details of the work support your viewpoint.
A literary essay may be your own interpretation, based only on your reading of the piece, or it may be a mixture of your opinions and references to the criticism of others, much like a research paper. Again, be wary of plagiarism plagiarism and of letting the opinions of more experienced writers swamp your own response to the work. If you are going to consult the critics, you should reread the literary work you are discussing and make some notes on it before looking at any criticism.