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 a way to study complex spaces by breaking them down into simpler, more manageable pieces. In a fiber bundle, the total space can be thought of as a collection of fibers that are "glued" together over the base space. This concept is widely used in various fields, including topology, differential geometry, and theoretical physics, to analyze and understand the properties of complex systems.