An agar plate is a Petri dish that contains agar and some nutrients (food for the microorganisms). It is used to grow microorganisms. For example, a blood sample of a patient may be put on agar plate, to let the bacteria that made him sick grow. These bacteria can then be identified using a microscope to let the doctor choose the appropriate treatment of the patient.
When microorganisms grow on the agar plate, they form colonies. Each colony has similar genetic characteristics.