Amethyst is a variety of quartz that is purple in color. It can range from a very light, almost clear color, to deep, dark purple that looks like grape jelly. In fact, there is actually a beautiful variety of amethyst from Uruguay that is called "grape jelly amethyst" for just that reason.
Even though amethyst is a variety of quartz, it is so well-known that it almost considered to be in its own category. Amethyst is generally abundant in the market, so you can find nice chunks, clusters, geodes, points, and tumbled pieces for a reasonable price. Of course, as with many stones, there is a range of grades (levels of quality) of amethyst - and prices vary accordingly.
Since amethyst is a variety of quartz, it is a silicon dioxide (SiO2). However, we know that, since it's not colorless like quartz, it has additional minerals in it, as well, including iron and manganese. Irradiation - or small amounts of radiation that naturally occur within the Earth - also influences the color of amethyst. This kind of natural "cooking" is nothing to worry about with your crystals! Mama Earth knows what she's doing ;)
Amethyst grows in various shades. Some, like the ones from Vera Cruz in Mexico, have a pale violet color. Others can be more vivid, and some are a deep, dark purple. Usually, the darker the tone, the higher the price. It's a good idea to keep this stone away from direct sunlight: it can fade with exposure.
Amethyst can be found around the globe. I've already mentioned that beautiful, dark pieces are found in Uruguay; but gorgeous amethyst is often found in Brazil, Madagascar, Turkey, Morocco, Canada, Mexico, and the U.S. (as well as in many other countries).
Most notably, amethyst is known the birthstone for February. Amethyst is also related to the astrological signs of Pisces, Virgo, Aquarius, and Capricorn (Melody, Love is in the Earth).
It is a stone associated with the crown chakra, which is located at the top of the head. As such, it is said to be a connection to spirituality and the divine, as well as helping to increase intuition. Amethyst is said to be a stone that is good for everyone - a crystal "jack of all trades," in a way. It is said to be good for balancing the left and right hemispheres of the brain, to help one be balanced on all levels.
Amethyst is also said to help with insomnia and bad dreams (Ken Harsh, Karma Crystal Guide to Stones). According to Philip Permutt's The Crystal Healer, amethyst also helps with "negotiation skills, decision-making, wealth, business success, moving forward in life, coping with responsibility and change, and public speaking."