Olives gained their greatest fame from the oil pressed from them.

An excerpt from the article 21 facts about olives

Olive oil called olive oil is pressed from the ripe, black fruit. Oil pressed from the first pressing, without heating or using increased pressure is referred to as "extra virgin "and is the best table oil. Subsequent pressing yields an oil of inferior quality - kitchen oil. The third pressing, which involves heating the fruit or adding hot water to it, yields the worst quality oil, for non-food purposes.