Your hands are all over your mouse and keyboard. Consequently, these peripherals tend to be loaded with bacteria that collect over time. Some of it can be harmful and could potentially cause illness to you and anyone else who ever uses your devices.
Perhaps the easiest method to clean your peripherals (and anything else you frequently touch) is to use paper towels or microfiber cloths with rubbing alcohol, which you can buy from any pharmacy. Apply the alcohol to the cloth and rub everything down thoroughly. Make sure to get in between cracks and small spaces where bacteria might collect.