Aha! I get it.

Thanks to Mama Hen from At A Hen's Pace, I finally understand cousins:

Your mother's cousin would be your first cousin once removed. Someone explained to me that it's like a many-layered cake. The top layer are the first cousins. Their children are in the second layer, and THEIR children are in the third. Everyone in the second layer are second cousins to each other, everyone in the third layer are third cousins. If you cross a layer though, it's once removed--two layers, twice removed. So you are the first cousin once removed of your mother's first cousin; your children are her first cousins, twice removed. If she has children, they are your second cousins; they are your children's second cousins, once removed.