What do College Institutions like to see on a student's college admissions essay?

Keep in mind that college admission essays are not one size fits all.
College Admission Officers first and foremost like to see that you have answered the prompt(s).
They want to see that you have taken the time to show commitment and preparation in the process.  Have you paid attention to grammar, punctuation and typos?
They want to see authenticity, that these are your words and not a scrubbed version of someone else's heavy editing.

It is your opportunity to have your voice heard.  
Colleges can interpret your academic history, trend in grades, activities and outside interests in the fill in the blanks portion of your application.  What they can not interpret are your personal characteristics and how they translate into:

• Grit - Did you have any challenges?  If so how did you overcome them? What lessons did you learn?
• Enthusiasm - What excites you and why?  What motivates you to keep doing what you do?
• Values - What is important to you and how do you portray and carry that out?
• Goals and aspirations -  Discuss your goals,  what steps you have taken to achieve them and why they are important to you.

I always tell student that after reading an essay, a college admission committee should be able to note 3 - 4 key things about you, and your personality. They should have enough information to determine if you would be a good fit for the college and what you could contribute to the campus community.  Can they determine characteristics like leadership, compassion, ingenuity from your essay?  Remember you will not be able to interview for every school you apply to... so your essay acts as an interview itself. 
Keep in mind as you write what are the take aways you would want an interviewer to have when describing you.
These take aways should come across in your essay.