I’ve been doing some genealogy recently and here’s some information about cousin relationships.
There are two different parts to the relationship definition. One is the degree of cousinship; first, second, third, fourth, etc. The second is the remove; once removed, twice removed, thrice or three times removed, etc.
Here is the degree:
First cousins share one set of grandparents. Grandpa and Grandma have more than one child. The children of those children are first cousins.
Second cousins share a set of great-grandparents. Your children and your cousin’s children are second cousins.
Third cousins share a set of great-great-grandparents. Your grandchildren and your cousin’s grandchildren are third cousins.
Fourth cousins share a set of great-great-great-grandparents. Your great-grandchildren and your cousin’s great-grandchildren are fourth cousins.
This continues on generation after generation.
Now for the removes.
Each remove is a generation. Your cousin’s children are your first cousins, once removed. They are your childrens’ second cousins.
Your cousin’s grandchildren are your first cousins, twice removed. They are your childrens’ second cousins, once removed. They are your grandchildrens‘ third cousins.