First Cousin: A child of one's aunt or uncle.
Second Cousin: A child of a first cousin of one's parent OR IN OTHER WORDS, A child of one's first cousin; a first cousin once removed.
Third, Fourth and Fifth Cousins: Your third cousins have the same great-great-grandparents, fourth cousins have the same great-great-great-grandparents, etc.
Removed: indicates that the two people are from different generations. You and your first cousins are in the same generation (two generations younger than your grandparents) so the word “removed” is NOT used to describe your relationship.
The words “once removed” mean that there is a difference of one generation. For example, your mother’s first cousin is your first cousin, once removed. This is because your mother’s first cousin is one generation younger than your grandparents and you are two generations younger than your grandparents. This one-generation difference equals “once-removed.”
Twice removed means that there is a two-generation difference. You are two generations younger than a first cousin of your grandmother, so you and your grandmother’s first cousin are first cousins, twice removed.