The Ideal Class Group is a concept in algebraic number theory that helps classify the ideal classes of a number field. It is formed by taking the set of fractional ideals of a ring of integers and grouping them into equivalence classes. Each class represents a unique way to factor ideals, which is crucial for understanding the arithmetic properties of the number field. In this context, an ideal is a special subset of a ring that allows for division by its elements. The Ideal Class Group measures the failure of unique factorization in the ring, providing insight into the structure of the ring and its associated number field, such as Q or Z.