Is it possible to completely delete(clean-up,format) that part of the hard drive that holds the 'emptied recycle bin' information without formatting the whole of the hard drive? I believe that when the 'Recycle Bin' is emptied,the information being removed actually stays on the hard drive in a place that is especially reserved for this function. Mine now has several gigabytes in it and I would like to completely remove it from the hard drive without affecting any other part of the hard drive.
When you hit the delete button data it is sent by default to the recycle bin, from here you can restore it if needed at a later date, when you Shift+delete the file bypasses the recycle bin and cannot be restored. The recycle bin is like temporary delete storage for files in case of unintentionally deleting the wrong file. Deleting the contents of the recycle bin should be enough to free up space on your drive.
All data on a drive is not deleted but instead the reference to where the data is kept is freed up for the system to overwrite that part of the drive, specialist software can retrieve this deleted data, data recovery firms use this software to recover hard drives for people who cannot access the information on their drives, therefor anyone with the software can read a formatted drive and retrieve personal information, that's why they say to physically destroy the drive when you sell a computer or use a program such as drivekill to overwrite it multiple times to make it harder to recover data. If you want to permanently delete a file then use Eraser as bremner suggests, it overwrites the file multiple times with random data in order to effectively destroy it.