The Gromov-Hausdorff distance is a way to measure how far apart two metric spaces are from each other. It does this by considering all possible ways to embed these spaces into a common space and finding the smallest distance between corresponding points. This concept is useful in various fields, including geometry and topology, as it helps compare different shapes and structures. This distance is named after mathematicians Mikhail Gromov and Felix Hausdorff, who contributed to the understanding of metric spaces. The Gromov-Hausdorff distance can be particularly valuable in areas like shape analysis and data science, where comparing complex structures is essential.