Hi,
I would absolutely highlight the app - what a great achievement.
Failure in businesses, particularly ones where you have got nothing more than an app, is extremely common (the rate sits at more than 99%). It goes to show your entrepreneurial spirit and taking risks.
If anything, just focus on the lessons learnt and how you would do it differently now with hindsight and also how this will change with an MBA degree will go a long way not just in your applications but also in your life. Studying an MBA equips you with structured thinking, functional and general management knowledge, stakeholder management, time management skills and gets you to exercise the brain cells you didn't think you had, what it doesn't do is to give you a business idea. Sure, it helps to expose you to different ideas that have worked which can help you generate new (and better) ideas and assists you in realising how to think about exploring different ideas but your idea is still your own.
Hope this helps,
If you need to discuss anymore or how to demonstrate this in your essays, please don't hesitate to contact me.
Indy