@SuperTouhou
It's a very literal name. The Replay Mod is a forge mod that allows users to record a replay of their play session in a Minecraft world or server (from when they login to when they logout). Using a recorded replay, users can access the built-in replay viewer and editor to tweak with the replay however they wish. Move the camera, slow down the replay, add props (images and text) to add flavour to your replays... Whatever!
From there, players can upload their edited replay to the Replay Mod servers (for other mod users to watch and play with) or they can render the replay and convert into actual video footage for use in video editors or to be uploaded directly to YouTube. Fun fact: Replay Mod supports 360 video and can actually be used on YouTube.
Check it out!Katrix's video is but one prime example of how the Replay Mod can be used. As you can see in the video, Katrix employed multiple camera angles and a slow playback speed which is built into the mod's Replay Viewer. There is a lot of creativity to be had with the Replay Mod. From simple replays of minigames to montages and machinimas, the Replay Mod is a brilliant tool in Minecraft.
That said, Replay Mod should be used wisely. With a great tool like this, it can also be abused. I won't say how but I already know a very obvious exploit with the mod. This is why I have discussed the mod in minimal quantities.