Understanding the proper terms for family relationships, such as second cousins or cousins twice removed, may sound confusing. However, the rules for each relationship term are actually simple.
The first relationship in the chain is the first couple, or common ancestor, in a line of relatives. The children of that couple are siblings (brothers and sisters). These rules apply for half-siblings also who share only one common ancestor.
The children of two siblings are first cousins. In other words, Genealogy.com says that children who are not siblings, but have at least one common grandparent, are first cousins. To put it another way, your aunt's or uncle's children are your first cousins.
The children of first cousins are second cousins. Ancestry.com points out that this means second cousins have a common great-grand parent.
Each next step down with children in the same generation creates the next level from third to fourth cousins and more. Therefore, fifth cousins had a common ancestor five generations back.
The slightly complicated part is the cousins "removed" which occurs when relatives are not from the same generation. In simple terms, Genealogy.com explains that the child of your first cousin is your first cousin once removed. That person's child is your first cousin twice removed. The child of your second cousin is your second cousin twice removed and so forth.