Calabi-Yau manifolds are complex geometric shapes that arise in string theory and other areas of mathematics. They are characterized by their ability to support Ricci-flat metrics, which means they have no curvature in a certain sense. These manifolds are typically six-dimensional and can be compact, allowing them to play a crucial role in the compactification of extra dimensions in theoretical physics. In string theory, Calabi-Yau manifolds provide a way to unify the four known forces of nature by allowing additional dimensions beyond the familiar three of space and one of time. Their intricate structure can lead to various physical phenomena, including the types of particles and forces observed in our universe.