A first cousin's child is known as a first cousin once removed because the offspring is one generation removed from the cousin. First cousins are in the same generation because they have the same grandparents on one side of their families.
Someone who is twice removed has a two-generation difference in relative terms. A person who is two generations younger than a grandmother's cousin is the first cousin twice removed of the grandmother's cousin.
Second cousins have the same great-grandparents, but not the same grandparents. Third cousins have the same great-great-grandparents, and fourth cousins have the same great-great-great-grandparents, and so on.