Group velocity refers to the speed of the peak intensity of a wave group, while phase velocity is the speed of individual waveforms, such as sine waves. In non-dispersive media, both velocities are equal, but in dispersive media, they differ, causing wave shapes to change over distance. Group velocity is always less than or equal to phase velocity and is significant for understanding energy propagation and information transfer. An interesting phenomenon occurs in thin metal foils where light can exceed the speed of light in a vacuum due to the properties of group velocity. This relationship is crucial in the study of photons as energy pulses, reinforcing the importance of wave behavior in various media.