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. 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.
Nephew and niece Facts for Kids. Kiddle Encyclopedia.