I have seen the terms "virgin" and "extra virgin" on bottles of olive oil. What do these terms mean, and how do they affect the flavor and cooking properties of the oil?
In the US, "extra virgin" isn't a legally protected term - some of the stuff sold as EVOO here would never, ever pass as it elsewhere.
Cooking-wise, the extra virgin stuff is best used in situations where it won't be highly heated. Salad dressings, dipping oils, finishing a dish, etc. are where it shines.
There are typicality four types of olive oil available, with Extra Virgin being at the top of the quality tree:
Extra virgin olive oil is mechanically pressed (you may see the term cold pressed) rather than being produced by chemical means. I has an acidity level of less than 0.8%. It is also tasted for flavour before being certified.
Fine or Virgin Olive Oil has an acidity of less than 2%. It often uses slighter riper olives. Olive oils with the low acidity of extra virgin but which haven’t passed the official taste test also fall into this category.
Ordinary Olive Oil is usually used to produce refined oils with a bland flavour.
Pomace Oil is processed from the paste left after the first pressing. It is generally quite flavourless and of low quality, usually only used for deep frying.
Exceptional quality Extra Virgin olive oil is still made on hand presses and hence the cost can be quite high.
The International Olive Council (IOC) and the United States Department of Agriculture (USDA) have standards for what constitutes "Extra Virgin" olive oil. It's based mostly on measurable chemical properties, but also some more subjective "sensory" criteria.
If you really want to geek out and know the details, there is a recent study by the UC Davis Olive Center that you should read. They tested major North American brands of Extra Virgin olive oil to see whether they meet the criteria to carry the designation. The results were quite poor.
The paper goes into quite a lot of detail about the specific criteria. Get the PDF at http://www.olivecenter.ucdavis.edu/news-events/news/files/olive%20oil%20final%20071410%20.pdf.