Computer recycling means taking things from old computers and using them in new computer things. The phrase is also used to mean that computers need to be thrown away in a special way, as they often have things that are bad for the environment or dangerous inside them that can cause problems if they are thrown away like usual waste (garbage).
Sometimes people are worried that the information inside a computer will be stolen when the computer is thrown away. For example, if you have a product design on an old computer, somebody might copy your design. Big companies have a lot of computers, with a lot of private information on them. They will often pay other companies to remove all the information from a computer before it is thrown away. This usually involves physically destroying the drive. It is possible to non-destructively erase the data on a hard drive by overwriting the entire drive with random numbers. With this method, only the data is destroyed, not the drive itself. This allows the drive to be reused.