A principal bundle is a mathematical structure that consists of a total space, a base space, and a group that acts freely and transitively on the fibers. It provides a way to study spaces that have a symmetry described by a group, such as the rotation group in physics. The fibers are the pre-images of points in the base space, and they represent the different states or configurations associated with each point. In a principal bundle, the group acts on the fibers without any fixed points, meaning that for each point in the base space, there is a unique fiber corresponding to each group element. This concept is essential in various fields, including differential geometry, topology, and theoretical physics, particularly in the study of gauge theories and general relativity.