Your grandfather's brother is your great-uncle, and you are his great-nephew or great-niece. Your great-uncle's children are your second cousins because you share common great-grandparents, just as you share common grandparents with your first cousins.
Aunts and uncles are the siblings of a person's parents. Siblings of grandparents are great-aunts and uncles, while great-great-aunts and uncles are siblings of great-grandparents, and so on down the line. The child of a person's aunt and uncle is that person's first cousin. If the first cousin has a child, then it is the first cousin once removed of that person because it is one generation away from their common relative.