A chestnut or chestnut tree is a tall tree with broad leaves.

Chestnuts are the reddish-brown nuts that grow on chestnut trees. You can eat chestnuts.

Something that is chestnut is dark reddish-brown in colour.

If you refer to a statement, a story, or a joke as an old chestnut or a hoary chestnut, you mean that it has been repeated so often that it is no longer interesting.