A state of being so technologically backwards/unlucky/unaware that all of your electronic devices, if any, are too outdated to support apps.
App is shortened form of the word 'application,' a term used to describe a specific type of program, coined by Apple Computers with the introduction of the iPhone.
Him: "I have never played Angry Birds."
Her: "You should download the app. Its a fun game"
Him:"I can't. My phone is so old it doesn't support apps."
Her:"That sucks, dude! You're appless."