Now your assignment is written, it's looking good, so it's time to hand it in, right? Wrong. I'm afraid you've just written the first draft, you still have one of the most important stages to complete: 'polishing'.
Proof-reading and editing are part of the 'polishing' process: they allow you to improve your essay and make it shine. These things are often neglected by students, but they're vital parts of the writing process. The ability to evaluate and improve upon your work is a university-level skill, and you'll be expected to demonstrate it.
You'll need to edit your work on two levels: macro-editing involves looking at the big picture: what does it look like on the page? Is there a strong, clear structure? Is there an obvious discussion or argument running through the assignment, or is it simply a description? Micro-editing involves looking at the details, including the grammar, punctuation and spelling.