Or, more to the point, what is "awesome"? Well, something that fills one with awe. But what is "awe"? According to Dr. Dacher Keltner (Born to be Good), "awe" is a feeling of uplifting that one gets when he is looking on things from up high. It's a feeling we get when we suddenly see our world and ourselves in a much larger scope; when we come to some understanding of our place, our path, and our purpose in our universe. Since time immemorial, it's a feeling we've associated with divinity.
It's hard to say what fills others with awe, but to be awesome from your own perspective is to do something that would fill you with awe. To "be awesomer" then is to be do more of that thing which fills you with purpose and meaning and (since your time and resources are finite) to do it at the cost of all the other things that just grind away at your life yet you feel no purpose, meaning, or self-actualization from.
So, what does "be awesomer" mean when translated out of uncool-high-school-faggotnese (and, incidentally, into cult-of-TEDnish)? It means to take a risk, abandon the beaten and grinding path, and to live a life that feels meaningful to you. If you ask me, that's sound advice; possibly irresponsible if you're a parent with kids depending on you, but definitely solid otherwise.
However awesome you think you are you need to appear more awesome than that to get into Y.C. :-)
I think the same approach would be useful for a YC application. Get other people to critique it, and iterate and improve. The trick is picking good reviewers. Probably more people can review copy than a YC application but I hear YC founders are generally friendly and like to help.
I recently made the mistake of doing a rush application for my local TedX and didn't get picked for the audience. I should have applied the "awesomer" philosophy to that.
Now I am going off to work on that robot...
I do like fun, goofy language but I hard a hard time with it in this context. ..probably because I went into reading the article with a certain attitude that didn't match "awesomer".
oh well.. :)