A cousin is a relative that is the child of a parent's sibling, this is more specifically referred to as a first cousin.
More generally, in the kinship system used in the English-speaking world, a cousin is a type of relationship in which relatives are two or more generations away from their most recent common ancestor. For this definition Degrees and removals are used to further specify the relationship.
Degree measures the number of generations from the most recent common ancestor(s) to a parent of the cousin. If the cousins do not come from the same generation Removal is specified as removal measures the difference in generations between the two cousins. This is relative to the most recent common ancestor(s). When removal is specified each cousin is separated by a different number of generations from the common ancestor. In this case the degree of the cousin from the previous generation is used.
To illustrate usage, a second cousin is a cousin with a degree of two; there are three (not two) generations from the common ancestor(s). When the degree is not specified, first cousin is assumed. A cousin "once removed" is a cousin with one removal, or generational difference, namely the child of one’s first cousin or the first cousin of one’s parent. When the removal is not specified, no removal is assumed.
Various governmental entities have established systems for legal use that can precisely specify kinship with common ancestors any number of generations in the past; for example, in medicine and in law, a first cousin is a type of third-degree relative.
Basic definitions
People are related with a type of cousin relationship if they share a common ancestor, and are separated from their most recent common ancestor by two or more generations. This means neither person is an ancestor of the other, they do not share a parent (are not siblings), and neither is a sibling of the other's parent (are not the other's aunt/uncle nor niece/nephew). In the English system the cousin relationship is further detailed by the concepts of degree and removal.
The degree is the number of generations subsequent to the common ancestor before a parent of one of the cousins is found. This means the degree is the separation of the cousin from the common ancestor less one. Also, if the cousins are not separated from the common ancestor by the same number of generations, the cousin with the smallest separation is used to determine the degree. The removal is the difference between the number of generations from each cousin to the common ancestor. Two people can be removed but be around the same age due to differences in birth dates of parents, children, and other relevant ancestors.
Additional terms
The terms full cousin and cousin-german are used to specify a first cousin with no removals. The terms cousin-uncle/aunt and cousin-niece/nephew are sometimes used to describe the direction of the removal of the relationship, especially in Mennonite, Indian, and Pakistani families. These terms relate to a first cousin once removed, uncle/aunt referring to an older generation and niece/nephew for younger ones. For additional removals grand/great are applied to these relationships. For example, a cousin-granduncle is a male first cousin twice removed that comes from an older generation, and a cousin-grandniece is a female first cousin twice removed who comes from a younger generation. The term grandcousin is sometimes used for the grandchild of a first cousin, or the first cousin of a grandparent: a first cousin twice removed. The term kissing cousin is sometimes used for a distant relative who is familiar enough to be greeted with a kiss.
Gender-based distinctions
A maternal cousin is a cousin that is related to the mother's side of the family, while a paternal cousin is a cousin that is related to the father's side of the family. This relationship is not necessarily reciprocal, as the maternal cousin of one person could be the paternal cousin of the other. In the example Basic family tree, Emma is David's maternal cousin and David is Emma's paternal cousin.
Parallel and cross cousins on the other hand are reciprocal relationships. Parallel cousins are descended from same-sex siblings. A parallel first cousin relationship exists when both the subject and relative are maternal cousins, or both are paternal cousins. Cross cousins are descendants from opposite-sex siblings. A cross first cousin relationship exists when the subject and the relative are maternal cousin and paternal cousin to each other. In the basic family tree example, David and Emma are cross cousins.