Green amethyst, also known as Prasiolite, is a member of the quartz family and has the same structure as purple amethyst. Prasiolite is amethyst that has been subjected to heat - the heat turns changes the traditional purple to yellow - and very occassionaly to green.
Almost all green amethyst comes from a mine in Brazil where natural conditions were just right to turn the purple into green. You do get some lab made green amethyst where natural purple amethyst is subjected to controlled heat to turn it green.
The result is a lovely clear cool green, some of which is glass like, and others which are deeper in hue, which is becoming more and more popular in jewelry.