It is simple, your cousin is the son or daughter of an uncle or aunt. So if your mother's or father's sister or brother has a son or a daughter then they would be your cousin, first cousin that is. Got it? Good, because nothing comes easy in Genealogy.
There are actually four types of first cousins according to anthropologists. A cousin on the father's side is patrilateral while those on the mother's side are matrilateral. Then of course the children of your mother's sister or your father's brother are ortho-cousins (parallel cousins) or the children of your mother's brother or father's sister are cross-cousins. So now you have patrilateral and matrilateral ortho-cousins and patrilateral and matrilateral cross-cousins for your four relationships.
The English word "cousin" covers all four of these relationships and many languages place the ortho-cousins, and the cross-cousins in separate categories. In these such cases ortho-cousins are frequently the same as those denoting brothers and sisters. There is a smaller group of languages that places the ortho-cousins in one category and then distinguishes between patrilateral cross-cousins and matrilateral cross-cousins. Other languages use separate words for each of the four possible kinds of cousins; patrilateral cross-cousins, patrilateral ortho-cousins, matrilateral cross-cousins, matrilateral ortho-cousins.
Although most societies consider marriage between ortho-cousins to be incest there are actually those that consider it to be ideal and those that cross-cousin marriages are preferred or even obligatory.
And don't forget about 1st Removed ...
Relationship Terms
Sometimes, especially when working on your family history, it's handy to know how to describe your family relationships more exactly. The definitions below should help you out.
Cousin (a.k.a "first cousin")
Your first cousins are the people in your family who have two of the same grandparents as you. In other words, they are the children of your aunts and uncles.
Second Cousin
Your second cousins are the people in your family who have the same great-grandparents as you., but not the same grandparents.
Third, Fourth, and Fifth Cousins
Your third cousins have the same great-great-grandparents, fourth cousins have the same great-great-great-grandparents, and so on.
Removed
When the word "removed" is used to describe a relationship, it 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.