This college application essay could have been written by my 17-year-old self. In particular, the phrase "the immense satisfaction" is so moi that it almost hurts.
I've made small remarks in red, and a few general comments below.
It is no ordinary day. [good] The first day of school possesses its own special aura of excitement and childlike innocence. [not nearly as good as the first sentence. The diction in the second sentence is needlessly high, and you're getting sentimental ("childlike innocence" and high-falutin' (why not "has" instead of "possesses"?] Genuine smiles are spread across the faces of the teachers, and the spirits of the students are on a temporary high as they reunite with old classmates. The lively atmosphere brings out the best in everybody as they amicably share their summer stories.