Exotic lumber is simply exotic wood that is found around the world. Remember that the term exotic as it's used here in the US is not what is used in the rest of the world. Consider Mahogany is not considered "exotic" in it's native central America and Northern South American regions. This is because it's a material that is readily available in these markets. So don't let the term "exotic" fool you into believing the wood is in short supply, but only that it's not local to your area. Philippine Mahogany isn't really considered "exotic" in that part of the world either. Though it's still expensive, what makes a wood exotic should really be it's availability.
Still there are tree species through like the American Chestnut tree that should rightfully be considered "exotic" and even endangered. The American Chestnut Tree was once in very large supply found especially in the Appalachian mountains where some grew upwards of 100 feet and had diameters of 10 feet. At one time, it's thought that as many as 1 out of every 4 trees throughout the Appalachian forested areas were the American Chestnut trees. They were not destroyed by humanity however but a lethal plague chestnut blight, a fungal disease which destroys the bark tissues of the chestnut killing them. Some hard Rock Maples and even Oak lumber could be considered "exotic" depending on the current supply and availability.
When searching for exotic lumber, check to see where was it's area of origin and how was it obtained. Many exotic woods are removed from endangered rain forest areas around the world. These are NOT the materials anyone would necessarily want if they cared about the environment. More importantly however, there are many alternatives that are also considered exotic timber but have either been removed from managed tree areas or grown specifically for the world market. Teak, is a good example of an extremely hardwood that although originated in the rain forests, is now grown in many places as a crop to serve the market interest in this fine material. By selecting a farm raised product, you will be helping to maintain the rain forests while also providing a living to local peoples and still getting an extremely beautiful material that lasts a very long time.
From Birdseye maples, to indigenous oak, and Brazilian Cherry, Walnut, and Rosewood, are all beautiful materials to create high quality furniture that will last several lifetimes.
With a little care, it's possible to obtain some of the finest "exotic lumber" materials in the world while still considering the environment.