The replay channel is accessed through the network, and is dedicated solely to sharing the replays of players from around the world. This is also where you must go to unlock Evangelist Of The "X", that is a different solution all together however. This trophy is for watching replays through the replay channel 50 times (duh), in order to do this you can either download and watch replays or simply go to one of the specific channels. Personally, I had no luck with either the Elite or Character replays, however the new replays loaded up almost instantly.
The nice part about this trophy is that if you go to the new replay section, you can simply press X on a replay, and press it again to stream it rather than download it and watch it later. Another nice thing about this is that you can press start to skip the intros and once the match starts, you can press start to end the replay sending you back to the replay list. These don't have to be unique replays to count towards the trophy, so simply keep loading up the first video and quitting out until you reach 50. If you'd like to stop at some point and check your progress later, you can see how many replays you knocked out in the Player Data section of the main menu.