The child of someone's first cousin is considered to be that person's first cousin once removed. The kids of someone's first cousin's children are that person's first cousins twice removed. This label denotes the fact that the child is the person's first cousin, and the removed aspect specifies which generation the child belongs to.
For example, if Lacy is Carol's first cousin twice removed, this means that she is two generations away from Carol's generation. If two first cousins have children, these children are called second cousins. They are not removed because they are a part of the same generation. First cousins share the same grandparents, while second cousins share the same great-grandparents. Third cousins share the same great-great-grandparents.