The Merriam-Webster Dictionary gives us a basic definition of a nut:
(1) A hard-shelled dry fruit or seed with a separable rind or shell and interior kernel.
(2) The kernel of a nut.
What is a nut?
For many the nut is most often defined as the dry, one-seeded, fruit of any of various trees or bushes. It is often edible but might require some cooking to get there. In addition, nuts come in a shell. Usually a hard and woody or tough and leathery shell. The kernel in the middle of these fruits is also called the meat or the nut.
What is not a nut?
Strictly speaking, a peanut is not a nut, a sunflower seed is not a nut, a water chestnut is not a nut, a coconut is not a nut, and a pine nut is not a nut.
What is the common denominator? These items all have shells that encloses an edible and tasty substance. The peanut, sunflower seed, water chestnut, coconut, and pine nut are seeds or they have a hard shell. Not one of these foods have both of them. Arguably, these items are called nuts because they are hard-shelled fruits that will stay fresh for a long time without decaying. But that does not make them a nut. Some have argued that the soybean should be called the soy nut. Admittedly, when dried, toasted, and salted, the soybean has a good taste. Since soy is grows in a pod, like a pea, it will never be considered a nut.
Trying to define a nut?
In his magnum opus, The Oxford Companion To Food, Alan Davidson writes, “Nuts are impossible to define in a manner which would be compatible with popular usage yet acceptable to Botanists. In this book, popular usage is preferred. So, the groundnut (a legume, also called peanut) and the chufa nut (a tuber) are allowed to shelter under the umbrella word”. Furthermore, he points out that in some languages there is a lack of any such umbrella word.