Nancy Jenkins explains the differences between various olive oils. This book has some great info and recipes to guide you on a healthy way of eating. While she explains the types of olive oil and how to distinguish where the olives were grown, in summary she suggests using extra virgin olive oil as the process to simply squeeze healthy olives to extract their oil. Other ways of extracting oil is with chemical solvents which is used on olives not sufficiently high in quality to produce extra-virgin olive oil. With this process it's stripped of flavors and aromas, then a little extra-virgin oil is added. She suggests only using this for deep frying.
In The Mediterranean Diet by Marissa Cloutier and Eve Adamson, extra-virgin olive oil is further explained as the first pressing of olives. Oil should be kept out of the light and refrigerate any not consumed in one month.