What is a virgin olive?

Freshly harvested olives are squeezed, or pressed, for their oil. The very first pressing is known as the "extra virgin" pressing. That is where the name extra virgin olive oil (EVOO) comes from. EVOO is considered to be the finest, and most flavorful, but isn't appropriate for high heat cooking because the oil tends to smoke at lower heat. The second and third pressings produce a less flavorful, but sturdier, oil that is sold simply as olive oil. So, the term "virgin" doesn't describe the olive, it's describing the refinement process for the oil.