Fiber bundles are mathematical structures used in topology and differential geometry. They consist of a base space, which is a manifold, and a typical fiber, which is a space that is attached to each point of the base. This setup allows for the study of how these fibers vary smoothly over the base space, providing insights into complex geometric and topological properties. In practical applications, fiber bundles can model various physical phenomena, such as in theory of relativity or gauge theory in particle physics. They help in understanding how different fields, like electromagnetism or gravity, interact with the underlying space, leading to a deeper comprehension of the universe's structure.