Cleaning removes dirt, dust, crumbs and germs from surfaces or objects. When cleaning, you probably use soap (or detergent) and water to physically clean surfaces and objects. This doesn't necessarily have to kill germs. However, because you killed some of them, there are fewer germs that could transmit an infection to you.
Disinfection uses chemicals (disinfectants) to kill germs on surfaces and objects. Some common disinfectants include bleach and alcohol solutions. You will usually need to leave the disinfectant on surfaces and objects for a period of time to kill germs. Disinfection does not necessarily clean dirty surfaces or kill germs.