There are a variety of different woods used to make wooden chess pieces here is a sample of a few but certainly not all:
Briar wood defined: This type of wood is from the hard woody root of the briar Erica arborea; often used in making tobacco pipes.
Ebony wood defined: Species of ebony are from India, western Africa and Indonesia and is prized for its luxuriant, multi-colored wood grain.
Beech wood defined: Grain is straight, with a fine to medium uniform texture. Moderate natural luster.
Bubinga wood defined: Grain is straight to interlocked. Has a uniform fine to medium texture and moderate natural luster.
Walnut defined:Walnut is a straight-grained hardwood that varies from chocolate brown (from the center of the tree) to yellow (outer portion of the tree).
It's a very strong and stable wood that can take intricate carving.
Rosewood defined: Rosewood refers to any of a number of richly hued timbers, often brownish with darker veining.
Maple wood defined: Maple is a creamy white hardwood that sometimes has a reddish tinge. One of the hardest wood species, it can take a beating and look great for years.
Boxwood defined: Boxwood has a fine, even texture with a natural luster. The grain tends to be straight or slightly irregular.
Padauk is an exotic wood that is a bright orange or almost crimson wood when freshly cut, but oxidizes to a darker, rich purple-brown over time.
Sapele is an outstanding African hardwood perfect for projects that require incomparable beauty.
Sheesham wood defined: Sheesham known as Indian rose wood tree. This wood is hard, durable and long lasting.
Tagua nut has the look and feel of elephant ivory without sacrificing any elephants!
Burl wood defined: Burls result in a uniquely patterned wood, which is highly prized for its beauty. It is valued and sought after by artists, furniture makers and sculptors.
Birdseye maple defined: Bird's eye is defined as a type of figure that occurs within several kinds of wood, most notably in hard maple. It has a distinctive pattern that resembles tiny, swirling eyes disrupting the smooth lines of grain.