You want to discard

your old computer and want to securely erase the data from your hard drive.

What can you use to do this and what is the process called?

Before you do this, make sure you save your important files on a physical backup device. From what I'm hearing, your probably are referring to the process of reformatting your hard drive. You can reformat your computer or reinstall your operating system but they don't "completely" erase your computer. There are two ways I know to securely and permanently discard and erase your computer. One is to get a certified computer refurbish company or some other trusted company to completely erase it. The other option is to buy specialized software that completely deletes your information. Then if you want to discard the computer, there are special recycle companies that will recycle the computer.