Mommy and her "cousins" were talking about this the other day...I just needed to clear things up a bit for all of them:
For example, a person with whom you share a grandparent (but not a parent) is a first cousin; someone with whom you share a great-grandparent (but not a grandparent) is a second cousin; and someone with whom you share a great-great-grandparent (but not a great-grandparent) is a third cousin; and so on. The child of your first cousin is your first cousin once removed because the one generation separating you and the child (the cousin) represents one remove. You and the child are still considered first cousins, as your own grandparent (this child's great-grandparent), as the most recent common ancestor, represents one degree.