A circle bundle π:E->M is a fiber bundle whose fibers π^(-1)(x) are circles. It may also have the structure of a principal bundle if there is an action of SO(2) that preserves the fibers, and is locally trivial. That is, if every point has a trivialization U×S^1 such that the action of SO(2) on S^1 is the usual one.

bundle | group action | principal bundle