The first cousin of one's mother is referred to as one's first cousin, once removed. This phrase is also used to denote one's relationship with a first cousin's child. The phrase "once removed" specifies that there is one generation difference between the two relatives, while "twice removed" signifies members of a family that are two generations apart.
In terms of relationships between cousins, first cousins share a set of grandparents that can be either on one's mother or father's side. A person can also have second, third and fourth cousins. However, the difference between second and third cousins is that second cousins share a set of great-grandparents while third cousins are related through one set of great-great-grandparents.