I Find that this line is very true in the sense that every person that is reading your essay is not trying to see who has the best story but instead who are you, and what makes you unique.  i think this is the best advice, don't try to make yourself special just because, be who you are and portray your personality through your writing. 

The line "a Good essay always shows; a weak essay always tells" is a concept that is true in all real life situations.  we learned and had practice with this in acting class (yes acting), that it means a lot more if you show emotion rather than just saying i'm sad or happy.  i find that this is true for college essays too: in order to stand out you need to be the one that make the reader think and invision what you are saying; that is what would make you stand out.