A fiber bundle is a mathematical structure that consists of a base space, a total space, and a fiber. The base space is a manifold, while the fiber is a space that is attached to each point of the base. This setup allows for the study of how the fibers vary over the base space, providing a way to analyze complex structures in geometry and topology. In simpler terms, you can think of a fiber bundle like a collection of fibers (or threads) that are attached to a surface. For example, if the base space is a circle, each point on the circle has a fiber, which could be a line or another shape. This concept is important in various fields, including differential geometry and theoretical physics.