I am looking towards applying to Stanford and continually hear about intellectual vitality. What exactly is intellectual vitality and how can I develop mine?
You really shouldn’t have to develop intellectual vitality–not at this point–and you probably have it in some form. 
What do you enjoy doing? Why do you do it? How is it related to your sense of need for intellectual inquiry and personal development? What makes you truly happy, intellectually? Talking about unconventional things helps, but clichés that are done well are generally better than failed gimmicks.
Disclaimer: Take my advice in this post with a grain of salt. [I</a> was rejected](Stanford Class of 2020 REA Results Thread - #42 by collegederp - Stanford University - College Confidential Forums) by Stanford in the Restrictive Early Action program. 
@collegederp I am sorry to hear about you not getting in. Thank you for explaining “intellectual vitality’”. I still have two years until I apply, so I think I have some time to develop my “intellectual vitality”. Good luck in your college search.
It’s nice to see someone preparing themselves early. 
If Stanford is a top choice of yours and your family is able to financially support it, then you should definitely enroll in the Stanford High School Summer College program. I spent eight weeks there and was truly touched. The only downside is that you may fall into so much love with it that you’ll not want to go anywhere else. (That’s what happened with me, but I’m… moving on)
Yes! You can still work on your intellectual vitality. We develop it all the time. Every personally meaningful experience in your life could contribute to it. Do what you love. Explore classes, projects, work, extracurriculars. Whatever inspires you. For the purpose of the essay, you have to find something significant that would show the admissions committee your vitality.
People interested in being in an an environment that supports interest in the world.