I want to discard my old computer and want to securely erase the data from my hard drive what is the process called.

I believe the process is called High Level Format.

The process of securely erasing data from a computer hard drive is called wiping.

When you delete something from a computer, you don't "delete" it. You're just telling the computer to substitute a blank item in for the item you want to delete. With some fiddling, computer experts can retrieve the overwritten item from the computer, although it is so-called "deleted".