In the past, the olive paste was pressed several times. The first pressing gave the best oil, later pressings with hot water produced clearly poorer qualities. That is where the expression “first cold pressing” comes from.
Today, olive oil is almost always extracted with centrifuges in a single step. There is no second pressing. Under EU law, “first cold pressing” may only appear on the label if the oil was obtained below 27 °C in a traditional hydraulic press. The common term today is “cold extracted”.