A grand uncle, also sometimes called a great uncle, is the uncle of one's parent. As such, he is also the brother of one of a person's grandparents. To a grand uncle, a person is a grand nephew or great nephew.
There is some discussion among genealogists as to whether the correct term is "grand uncle" or "great uncle." In direct-descendant relationships, the term "grand" is used to indicate two generations removed, and "great" is used for each generation after that. Thus, a person's mother's mother is his grandmother, and her mother is his great-grandmother.
Using this model, the brother of one's grandmother would be that person's grand uncle, and the brother of his great-grandmother would be his great-grand uncle. However, some people use "great uncle" to describe the brother of one's grandmother.
Using the title of great uncle to indicate the brother of a grandparent can become even more confusing for the next generation. If the brother of one's grandmother is that person's great uncle, the question arises of whether or not the brother of his great-grandmother is his great-great uncle. Is such a case, for clarity's sake, one should refer to his grandmother’s brother as his grand uncle, so that his great-grandmother’s brother would in turn be referred to as his great-grand uncle.