Just to clarify, a replay system records data (object locations, rotations, and scale if needed), not images. This data can then be used to recreate a running game at a later time, so you can spectate it from any angle. If you wanted to make a video out of this, you would still need to use video recording software to capture clips, and video editing software to edit the clips into a full video.
So, let's say there was an epic, game winning flak shot everyone missed because they were watching the other battle. With replay, you can go back to that point and view it from new angles, replay it over and over, pause, rewind, and possibly use bullet cam.
This would also allow Muse to add 'MVP' repays at the end of a match, or post games and free view tutorials for people to watch (while waiting in lobbies).