Your data is safe and secured. The data you entered is stored on the Apple iCloud. This means if you upgrade the app or your phone, or use a different iOS device such as switching from an iPhone to an iPad, you will still be able to get at all your data.
There is no complicated sign-in process, no account creation and no password to enter or remember.
You do not need to worry about backing up your TennisKeeper data. If you deleted the app, just re-install it. As long as you log in to the Apple iCloud with the same Apple ID, you will see all your data.