Mahogany is a pinkish or reddish-brown type of wood commonly used in furniture. Mahogany is typically very smooth in texture, with few knots or voids, making it a desirable type of wood aesthetically, and easy to work with when building furniture or musical instruments. Mahogany is considered a part of the Swietenia genus of trees: Swietenia mahagoni, Swietenia humilis and Swietenia macrophylla. Swietenia mahagoni is the rarest sub-type and is native to Florida, parts of Central America and the Carribbean. The latter two can both be found in South America.
Press your fingernail into the wood to determine whether or not it's a soft or hardwood. If your fingernail leaves a mark, it is softwood. If not, it's a hardwood, which means it might be mahogany.
Observe the corners of the wood in order to determine if the wood is solid or a veneer. If you can see a thin layer at the end of the edge, it's a veneer, not mahogany.
Observe the pattern and grain. If the grain is fine and long, it might be mahogany, even if it might have a slight wave to it. Also, if you look close up and you see that there are many dark fine lines to the grain, that may be a good indication of mahogany, as well. These lines can be anywhere from 1/16 inch to an inch.
Observe the color. Though mahogany is mostly known for being a darker reddish-brown when varnished or stained, mahogany that hasn't aged much can be more pink in color.