If you've purchased an app from the App Store or Play Store, you won't have to pay for it again as long as you use the same Apple ID or Google account. However, if you delete the app, you will lose all your data. Fortunately, you can easily re-download apps from the App Store or Play Store. When you uninstall an app, the market will remember that you bought it.
It will show that you bought it on the market and you can reinstall it at any time. For example, when updating a ROM, you can go to the market's download section and see all the applications you've purchased. Reinstalling an application means uninstalling it from the phone and then reinstalling it. Uninstalling an application means completely removing it from the phone.
To use it again, you'll need to reinstall the app on your device. The installed application will look and behave the same as when you first installed it. That is, you will have to reconfigure the application. In short, you can use apps that you have previously purchased from the App Store or Play Store without having to pay for them again. This is especially useful if you've paid for an expensive app like Pages, which contains all your university work and won't be updated.