When you sterilize something, you make it completely clean and free from any contaminant. It's important to sterilize tools, hands, and furniture in hospitals so germs don't get spread between patients.
People who make their own jam and pickles need to sterilize the jars first, and when you feed a tiny baby it's important to sterilize the bottles. Whenever you need to make sure something is as clean as possible, you should sterilize it. The earliest meaning of sterilize is still in use, too: to "make infertile," or to make it impossible for an organism to reproduce or have a baby.