"This App" is damaged and can't be opened. You should move it to the Trash.

If you have just downloaded a new app and received this message upon attempting to launch it chances are it's fine, OS X is just being a good nanny.

To fix, open System Preferences... under the Apple menu. Open Security & Privacy then click the lock to make changes. Change your Allow applications downloaded from: radio selection to Anywhere and give it another spin.