Cold-pressed olives refers to the production of olive oil via a mechanical process during which the temperature of the olive flesh is kept constant using probes, which make sure it doesn’t rise above a particular point.
In accordance with EU Regulation 29/2012 on marketing standards for olive oil, cold-pressed olive oil must have been extracted at a temperature of less than 27° C.
The phrase “first cold pressed” can still be found on many products, even though it sounds out of place and anachronistic now that the technique is no longer used.
Originally, there were two stages to olive pressing, due to the fact that the old hydraulic presses were unable to extract all of the juice from the olives in one go. That’s changed now, so it’s more accurate to simply refer to “cold-pressed” oil nowadays.