Use BleachBit to remove your files.
Bleachbit is much like CCleaner, which I recommended for Windows users a while ago. I still recommend CCleaner for Windows Users, but since it’s Windows only, it isn’t useful for Linux users. You can remove files, shred files (Completly wipe them) and wipe the free space on the disk drive.
The reason that you would want to shred a file is to make it impossible to recover later. There are programs that can recover files that have been deleted, which is why you would want to ‘shred’ your sensitive documents.