If you've met a certain standard or proven that you're qualified for some specific job or task, you're certified. Most schools hire only certified teachers.
In order for a person to become certified, there is usually some sort of test or review. A certified accountant has proven that she knows how to prepare tax forms and other financial records by taking classes and an exam. A certified diver has trained to use scuba gear and dive to a certain depth in the ocean, and demonstrated this ability. When you're certified in some way, you often receive a certificate, a document that proves it.