In the literary essay, you are exploring the meaning and construction of a piece of literature. This task is more complicated than reviewing, though a literature review and a literary essay 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 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 and of letting the opinions of more experienced writers swamp your own response to the essay. 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.