We still have very little concrete information about the upcoming Xbox 720 that Microsoft will officially unveil on May 21. We do know that Sony is pushing the sharing of in-game video aspect with the PlayStation 4 and we doubt that Microsoft will miss out on the opportunity presented by this feature.
According to Polygon's sources, Microsoft's version will be a bit different. The Xbox 720 will feature DVR-like recording, allowing users to rewind and watch or share highlights. This feature will be able to be turned off or set to occur when certain triggers occur, such as a headshot or Achievement.
If Microsoft does tie this DVR feature into the Achievements system, it could be really cool. It would also mark one of the largest overhauls of the Achievement system, which currently does very little. These captured videos would then, of course, be able to be shared on sites such as YouTube.
Like all things, until an official confirmation is made, take this with a grain of salt.