Show don't tell:

You want to scream every time your English teach utters this elusive phrase, I know. But basically, just bear in mind the difference between saying, "I love math," and saying, "As I flipped open my new Calculus text, the butterflies in my stomach overwhelmed me with the desire to grab the nearest pencil and graphic calculator, to submit to exploring the concepts of limits and derivatives for the night's remaining hours." One of those statements is vastly more convincing (albeit immensely more melodramatic in this case) than the other. Focus on specificity and vivid details - captivate your readers with tributes to all five senses rather than vague references and empty declarations.

Be conversational rather than formal:

Admissions committees are interested in your voice and how you sound, so you can drop the stuffy act that you normally put on for your English and History teachers in the essays you submit to them. Be relaxed and casual - write as you would speak. However, don't get too comfortable. Keep it within reason and be appropriate - no cursing or vulgarities.

Proofread:

These page long extensions of yourself constitute the first and most vivid impressions you'll have a chance to make to the committees deciding your post-secondary fate. Typos and word omissions and clumsy wordings suggest that as a student, you are careless and do not take enormous pride in your work. In the same way you'd be embarrassed to encounter your crush with sleep-crust in your eyes or visible wax build-up in your ears; you should be just as embarrassed and take just as much care and precaution to ensure that college admissions committees see you at your very best on the page.

Step away, and then return:

The best way to proofread effectively and make fair assessments of how your own writing will come across to your readers is to give yourself some distance from the material long enough to be able to return to it as though it's new to you. Proofreading right after you've completed a draft may mean you've got the best of intentions, but while you're too close, you're bound to only read everything exactly as you intended. You'll never see where "its" should be "it's" instead, or where you meant to put "the" instead of "she." This is why beginning admissions essays the night before they're due (or, even worse, the night they are due) is never ever a good idea - make sure to leave enough time built into your process for proofreading to happen as critically as it needs to.

Have others review your writing:

Another way to get around being too close to your written work, and offer it the criticism it deserves is, to have another party that's not so close to the material to read it and offer you feedback. Consider all feedback thoughtfully - it all comes from somewhere valid - but do bear in mind that you do not have to take every single suggestion someone put forth. The more people you show your work to, the more points of view you'll get, and that's great - but be careful not to overwhelm yourself with too many varying perspectives. Remember that it's you who's making the final call when it comes to content and structure. But certainly you'd better listen when told you've missed a comma or spelled "opportunity" as "opportunity" instead.