When you delete something on a HDD, USB or Internal you're only deleting the link address to the location of the file on the HDD, that tells the HDD that it can write new data over that section, but depending on where its located on the HDD it may or may not be written over immediately.
Now if you have sensitive data on your HDD like for example your credit card number from online purchases you wouldn't want that waiting around on your HDD to be written over.
Programs like Internet Cleaner and Eraser are excellent file shredding programs that immediately overwrite files you may need removed from your computer, these programs shredding capabilities overwrite the files multiple times making it literally impossible to recover the files.
The recovery program I supplied a link to I've recovered files with from a HDD that was accidentally reformated all he will have to do to get his files back is have PC Inspector restore the directory link to his file, if it hasn't been written over and he should be able to go straight to the files on the HDD.
If the link cannot be repaired he will still be able to recover the file, PC Inspector is the best program I've used yet and best of all its free.