I believe it's their way of trying to scare you to keep the application installed. Since Carbonite is an online backup service, they're warning you that if you remove it, your files will no longer be automatically backed up, which is true. Yes, this does leave you more vulnerable if your hard drive fails or some other accident happens. If you're not using it, however, or don't wish to pay for it, then you can remove it - nothing will happen to your files just as a result of removing it. If you do need a backup solution, you could read our series here
which provides various backup solutions.