Cousin is a comprehensive term for a relative with whom one shares a common ancestor, but who isn’t a parent, grandparent, sibling, aunt, uncle, niece, or nephew. Cousins are collateral relatives, being neither direct ancestors nor descendants.
Degree
Degrees and removes are used to specify how two cousins are related. The degree is 1 less than the number of generations separating cousins from their last common ancestor. People who share parents (1 generation away) are brothers and sisters. People with the same grandparent (2 generations away) are first cousins (or simply cousins). People who share a great-grandparent (3 generations) are second cousins. The degree can be easily calculated by adding all of the greats and grands in the last common ancestor. A person with whom you share a great-great-great grandparent (3 greats + 1 grand = 4) is a fourth cousin.
Remove
First, second, and third cousins are all members of the same generation (falling into the same horizontal row in a family tree). For people in different rows, removes indicate how many generations separate cousins from one another. For instance, the child of your first cousin is your first cousin once removed. (So, by the way, is your mother’s first cousin.) In these circumstances, the member of the older generation (with fewer steps to the last common ancestor) determines the degree of the relationship. To calculate the remove, for each cousin, add the greats and grands of the last shared ancestor, as above, and take the difference of the two numbers. E.g., if Edna is Trevor’s great-great grandmother (3), and Marjorie’s grandmother (1), the smaller of the two degrees is 1, and the difference between the two degrees (3-1) is 2. This makes Trevor and Marjorie first cousins twice removed.
Family tree relative to self (orange), with cousins in green.
Wikipedia on cousins
Granduncle Mark on cousins