A nephew is the son of someone's brother or sister. A niece is the daughter of the person's brother or sister. To the nephew or niece, the person is their uncle or aunt. The gender-neutral word for nephews and nieces is nibling. The relationship of aunt/uncle to niece/nephew is an example of second-degree relatives, meaning that their coefficient of relationship is 25%. In some cultures and families, it is common to call the child of one's cousin a "niece" or "nephew". In old English, the son of one's sister was called a sister-son.
A grand-nephew (male) or grand-niece (female) is the child of someone's nephew or niece, the grandchild of someone's brother or sister. Grand-niece and grand-nephew are often inaccurately referred to as great-nephew or great-niece, as recently stated here.