Sometimes there are files that you want to make sure are gone, not just removed from the file index, but physically removed from the disk so they cannot be recovered even if you knew where they were on the disk. Some innocent examples include bank statements, credit reports or plain-text versions of files you wish to keep encrypted.
On Linux I use an excellent utility called wipe. It's brilliant for the information in its man page alone as well as the utility. There are options to specify how to go about wiping the files to be destroyed as well as advice on how this will affect the potential recoverability of the files.
In OSX there is a similar utility in the menu for the Trash can:
- Finder -> Secure Empty Trash...
It does not give options for how to go about destroying the files (as far as I can find) but seems to overwrite the file multiple times with what Apple claims is digital gibberish.