I'm confused about virgin and extra-virgin food and fibre.

I've seen bottles of "virgin" and "extra-virgin" olive oil. What does this mean? I have my suspicions: is it to do with the first harvest each year? or is it more to do with the processing of the fruit to get the oil? (in which case, is "extra-virgin" olive oil what you get after the first pressing? or after the ultimate pressing? how many pressings do olives get, anyway?!)

Then there's "pure virgin wool" (and no, "pure virgin" is not necessarily redundant!). What does this mean? Again, I have my suspicions: is it to do with the first shearing of a sheep? and if so, is it the first shearing in its lifetime? or, like, what?