Personally, as a gamer, the native replay system is the most exciting thing I've seen out of this generation. So many times I've been playing a game with my brother over Xbox Live and something awesome happens, and afterwards we're kind of like, "Man, I wish this game had a record button like Halo so we could watch that over and over again." And now they all will.
The feature Sony announced for the PS4 is actually more powerful than that - it not only records, but also allows live screen streaming and sharing gaming sessions with friends remotely. One of the use cases they suggested was being able to have a friend take over and help you out if you were having a particularly hard time with a section of a game.