Register is more important than tone or diction, and it's not talked about enough in English classes! (By the way, this is closely related to my post on the Two Yous!)
A common mistake
Many students write admissions essays like this:
In my summer program, I encountered myriad opportunities to discuss my conceptions of morality with my peers.
You probably know this is "too fancy," but what does that really mean?
Don't you want to be fancy to impress the admissions officers?
What makes this version "too" fancy?
How fancy can you be?
Ideal Approach
Register is the implied context for language. An easy example is written vs. spoken English.
School essay: 100% written
Talking to your friends: 100% spoken
Here's the tricky hybrid: The admissions essay should be spoken but well spoken.
Your goal is to create the illusion that narrator-you is sitting in the room with the admissions officers, telling them the story in person.
I recommend reading your essay out loud to see how comfortable you are with your wording.
Tips
A great style guide called The King's English has rules you can follow:
familiar > unfamiliar
deceit > chicanery
concrete > abstract
use > employ
one word > multiple words
use > make use of
short word > long word
walk > perambulate
Germanic > Latin
think > conjecture
You can Google a word to see its origin. For example, search "conjecture origin"
Further Reading
Virginia Woolf's A Room of One's Own is a fantastic (and very funny) essay in a conversational register: it feels like she is talking to us—and just happens to be an amazing speaker.
There are many registers besides just spoken vs. written. The Wikipedia article on register is great if you want more information.
– Aaron