Firstly, find out if it is softwood or hardwood. To do that, press your fingernail on the wood in some hidden place (you do not want to damage the piece). If your fingernail leaves a mark, it is softwood. If it does not, then it is hardwood. Mahogany is a hardwood.
Next, find out if it is solid wood or veneer (a thin layer attached to the surface of a less expensive wood). You can do that by looking at the corners. If you can see the edge of a thin layer, you are looking at a veneer.
If it passed the first two tests, look at the colour and pattern of the grain. Mahogany has a light brown colour if not stained but looks deep reddish brown when varnished, wet or stained. It takes a stain very well and there won't be a lot of contrast. The grain is fine (oak, by comparison, has a wide grain) and is long, luxurious and can have a wave to it.
Looking close up, you will see grain is made up of many many dark fine lines, from 1/16th of an inch to about an inch.
Of course, a picture is worth a thousand words, so look online for pictures of mahogany and compare it to cherry, walnut, oak, maple and pine.
Mainly by experience with different types of wood. Generally, mahogany is a deeper colored, dark brown wood. The grain is usually very tight, and the grain pattern may be difficult to distinguish. Cherry on the other hand is a more reddish colored wood with a very distinct grain pattern, typically with think dark and light lines.
Two images have been linked below for visual comparison. This is not always accurate, but may be helpful.
Mahogany can be a noun or an adjective. As a noun, it refers to a type of tree or its reddish-brown wood. As an adjective, it describes something that is the color of mahogany or made of mahogany wood.
Mahogany is a wood from the mahogany tree.
Mahogany is a type of wood, sweetie. -___________-
The mahogany table in the dining room gleamed under the sunlight.
Mahogany timber is natural. The wood comes from the tree, Swietenia mahagoni.
Mahogany timber is natural. The wood comes from the tree, Swietenia mahagoni.
Mahogany wood
The Nimbus 2000 is made of mahogany wood.
Wood, often mahogany or birch
This guitar is made mainly out of wood which is glued together. The Thunderbird bass is designed concurrently with the neck through which is made out of maple or mahogany wood. The body is made from mahogany wood while the fretboard is made from rosewood or ebony.
Most Gibson SG guitars are made of mahogany. I'm sure there are others but I can think of any. Warmoth makes custom guitar bodies made of any type of wood you want.
James Potter's wand is made of mahogany and is 11 inches long. It's core is unknown.