Mommy and her "cousins" were talking about this the other day...I just needed to clear things up a bit for all of them:
"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 between either cousin and the nearest 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, 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.
This is mommy's cousin...

These are mommy's first cousins, once removed.
These are my second cousins ('cause we share our great-grandma and great-grandpa Jones).

are you still confused???