Gromov-Witten Invariants are mathematical tools used in algebraic geometry and symplectic geometry to count the number of curves on a given algebraic variety. They provide a way to measure how many curves of a certain degree can be found within a specified class of shapes. These invariants arise from the study of moduli spaces, which are collections of geometric objects, and they help in understanding the relationships between different geometric structures. By analyzing these curves, mathematicians can gain insights into the topology and geometry of the underlying space, contributing to broader areas like string theory and mirror symmetry.