who's server does an app run from?

[Shopifeye]

Silly question, but to make an app you have to have your own server correct?

The most you can do w/o an app is using your template markup correct?

[Caroline_Schnap]

Yes, you have to have your own server.

If you develop your app using Ruby on Rails, you can deploy your app on heroku for free: http://heroku.com/pricing#blossom-1.