The Gromov-Wasserstein Distance is a mathematical concept used to compare two metric spaces, which can be thought of as sets of points with distances between them. It measures how similar these spaces are by considering both their geometric structures and the relationships between their points. This distance is particularly useful in fields like machine learning and computer vision for comparing shapes and distributions. Unlike traditional distances, the Gromov-Wasserstein Distance does not require the spaces to have the same number of points or to be embedded in the same way. Instead, it focuses on the optimal transport of points between the two spaces, allowing for a more flexible comparison that captures their intrinsic properties.