One's mother's cousin is that person's first cousin once removed. A once removed relationship is one that is the same relationship but one generation apart. The child of one's cousin is also one's first cousin once removed. This is frequently confused with the term "second cousins."
Second cousins are the children of one's parents' cousins. Second cousins share at least one great-grandparent. With first cousins once removed, the younger generation's great-grandparent is the older generation's grandparent.
Although uncommon, there is a relationship called double first cousins in which a pair of brothers marries a pair of sisters and have children. The children are double first cousins and have both sets of grandparents in common.