A cousin in English kinship terminology is a relative with whom one shares a common grandparent or more distant ancestor, and who is not in one's own line of descent. The term cousin never applies where there are other specific terms to describe relationships.
A system of degrees and removes is used to describe the relationship between the two cousins and the ancestor they have in common. The degree (first, second, third cousin, etc.) indicates the minimum number of generations separating either cousin from the common ancestor; the remove (once removed, twice removed, etc.) indicates the number of generations, if any, separating the two cousins from each other.
For example, if person A and B share a common great grandparent, they are second cousins, because two generations (the parents and grandparents) separate each of them from the great grandparent.
If person A's great grandparent is person B's grandparent, then they are first cousins once removed, "first" because there is only one generation between B and his or her grandparent and "once removed" because there is a further generation between A and that same ancestor.
The system can handle kinships going back many generations. In 2004, genealogists discovered that U.S. Presidential candidates George W. Bush and John Kerry shared a common ancestral couple in the 1500s. It was reported that the two men are sixteenth cousins, three times removed. However, the two are in fact ninth cousins, two times removed.