When something has a designation, it has a title or a description that helps you identify it. The “organic” designation on the vegetables you buy lets you know that no pesticides were used in growing the plants.
Designation can refer to a title, official or otherwise. You may earn the designation “class clown” for your goofiness, or ask your friends to refer to you by the designation, "Madame Super Brain." Designation is also the act of assigning such a title or position, like the designation of your daughter as heir to your estate. Often, designation refers to giving a formal position. The district board may be responsible for the designation of the next principal at your school.