What is revising? Writing is only half the job of writing. What's the answer to this riddle? Well, the writing process begins even before you put pen to paper. And, once you finish actually writing, the process continues. What you have written is not the finished essay, but a first draft--and, as you go over it each time to improve it, a second draft, third draft, as many as necessary to do the job right. Your final draft, edited and proofread, is your essay, ready for your reader's eyes.
Remember, though, that revision of an essay is not simply proofreading. Proofreading is checking over a draft to make sure that everything is complete and correct as far as spelling, grammar, sentence structure, punctuation, and such matters go; it's a necessary, if somewhat tedious and tricky job, one that a friend could help you with--even if that friend is a "Spellcheck" on a computer. No machine can help you with true revision, however, nor would you want it to--a re-vision of your essay, how you see things now, deciding whether your thesis and body, and also your introduction and conclusion, really express your vision.
Revision is global, taking another look at what ideas you have included in your paper and how they are arranged; proofreading is polishing, one spot at a time. That's why revision should come before proofreading: why polish what you might be changing anyway?