That depends, mainly on the media that the data is on.
For example a WORM or Write Once Read Many drive like a CD or DVD can not be erased as the data is burned into the disk. The easiest way to securely erase data on these devices is to shatter the disk or shred it. However, hard drives, flash drives, flash memory, floppy drives, solid state drives, floppy drives, external drives and other types of read/write data storage devices.
You might be wondering at this point what is a secure erase. After you empty your files from your recycle bin or trash can your files are no longer visible. However, while the pointers to the data are gone, the actual information remains. Using the right software, data can be recovered from a disk, even after it has been formatted and had an operating system reinstalled.
A few different methods of securely wiping data exist. The easiest is to download, burn and run a software package that wipes the entire drive using multiple passes of random information. DBaN is our favorite software for this as it boots quickly and is easy to use. Do keep in mind however that this will leave the computer unusable unless the operating system is reinstalled. While this method takes a long time (about 5 hours for a small hard drive) it uses algorithms that the DoD and other government agencies developed to securely wipe media.
To wipe just a few word documents and not your entire computer, you need something a little more focused than a boot and nuke style wiper. Our recommendation for this kind of use is a program called Eraser. This will find the file on the hard drive and write random data over it several times to make sure your data is safe. You can even schedule the software to securely wipe the contents of a folder. Do note though that solid state drives can be next to impossible to selectively erase just one file due to wear leveling and other systems used on this technology.
The last option to secure your data is to use a large hammer. Seriously.
As a reminder, this software is designed to make the data completely unrecoverable, care must be taken to ensure that the correct information is targeted.