Complex sentence: A fibration is like a fiber bundle, except that the fibers need not be the same space, but that instead satisfies an additional condition guaranteeing that it will behave like a fiber bundle from the point of view of homotopy theory.
Split into simpler sentences: A fibration is like a fiber bundle, except that the fibers need not be the same space, rather they are just homotopy equivalent. Instead, a fibration satisfies an additional condition guaranteeing that it will behave like a fiber bundle from the point of view of homotopy theory.