The concept of "virgin" olive oil is actually quite simple. It means the oil was fresh-squeezed from the olive!
Technically it means the oil was mechanically extracted from the olive. Many oils are chemically extracted with solvents such as hexane, so that's not allowed for virgin oil. It also means that the oil has not been treated after production to remove flavor defects in a process called refining.
The "Extra" in Extra Virgin means the olive oil has "perfect flavor".
An olive oil is "virgin" if it's been freshly squeezed from the olive, but that doesn't mean it tastes good. The olives could have spoiled before pressing creating unpleasant "winey" or "fusty" flavors, or the oil could have oxidized after pressing creating stale "rancid" flavors.
Today, "first pressed" simply means that the oil was mechanically extracted in one pass, so it's actually redundant to say First Pressed Extra Virgin.
(AN INTERESTING FACT: "First pressed" used to refer to the old olive mill presses and how many times the olives were literally pressed, but today nearly all olive oil is spun in a centrifuge so there is no second pressing.)
Gently heating crushed olives is a normal part of high-quality olive oil production, BUT heating too much creates flavor defects, so "cold pressed" means olive oil not heated above 30°C (86°F) during milling.
All true Extra Virgin Olive Oil is "first cold pressed", so while it sounds good, you don't need to look for it on the label.
There is a long list of chemical criteria (like free-fatty acid or peroxide value) used for testing olive oil, but they do not have anything to do with the meaning. They are simply enforcers of the Extra Virgin standard and that's a whole separate email ;)