Moduli spaces are mathematical structures that classify objects up to certain equivalences, such as isomorphism. They provide a way to organize and study families of geometric objects, like curves or surfaces, by representing them as points in a higher-dimensional space. Each point in a moduli space corresponds to a specific object, while the structure of the space captures the relationships between these objects. For example, the moduli space of curves can help mathematicians understand how different algebraic curves relate to one another. By analyzing these spaces, researchers can gain insights into the properties and behaviors of the objects they represent, facilitating deeper exploration in areas like geometry and theoretical physics.