Scientists from NASA have found that a large region of our universe is moving in a particular direction using observations of the cosmic microwave background and X-ray clusters. It seems that the local region of our universe, at least a couple of billion light years across, is moving towards a particular patch of the sky relative to the cosmic microwave background.
Gravitational models of the observable universe are not able to account for such a large-scale "dark flow", so they are speculating that the motion might have been due to the pre-inflation gravitational attraction from mass outside the observable universe. From what I can gather, it seems that an uneven distribution of mass and energy throughout the universe set our particular region of the universe moving slightly towards a specific direction. This would have been before the inflationary phase of the Big Bang. After going through inflation, the masses responsible for the gravitational attraction would have moved too far away for any gravity from them to reach us. And yet our local region of the universe would still maintain the motion due to inertia.
I could have misunderstood what the scientists were saying, though, so any corrections would be welcome. In any case, if there really is such a "dark flow", which should be confirmed with further astronomical observations, then it's mind-boggling in that it might give some of the first hints of what the outside of our observable universe looks like.