Gemstone stability usually defines the ability for a gemstone to remain its natural color without changing easily or abruptly. While many gemstones such as diamonds are usually extremely stable and will not change color, other gemstones are not as stable and can be affected by many types of stimuli, usually being intense heat and radiation, which can come in the form of sunlight.
Usually microcrystallines are more susceptible to stability issues and two of the more popular gemstones that are less stable and more apt to change colors due to heat and radiation are Amethyst and Topaz.
Less stable gemstones usually have what is called color centers. Color centers are within a gemstone and can include tiny amounts of trace minerals. While not fully understand, these trace minerals or elements can change the color of the mineral rather easily.
For instance, much of the Citrine that is purchased in jewelry stores was once Amethyst that has been heated to a certain temperature. Once at a certain temperature, the violet or purple of Amethyst changes to yellow.
Topaz is another unstable gemstone. Most Blue Topaz on the market today was once either colorless Topaz or Yellow Topaz. It is heated and turns other colors, most notably blue.
Usually when the colors are changed commercially they are labeled as enhancements. Practically all jewelers will state whether a gem has been enhanced or not.
While gemstones can be enhanced commercially, it is possibly for gemstones to change color on their own, usually when they come in contact with light. Many gemstones can become more colorful or less colorful depending on the radiation.