>>12400932A dumbed down version:
when an object is moving through space it has a velocity (as well as quantum spin, gravity, etc.) When that object bumps into another object, it transfers some of that velocity to another object and changes the second one's velocity. Theoretically, you could look at the second object's trajectory and trace it backwards to see exactly when/how hard the first object bumped into it. This is what they mean by transferring information - the first object transferred some of its momentum to the second object and that information is preserved via the laws of conservation of momentum.
Now when an object hits the event horizon of a black hole, some of the information is preserved (I forget exactly which properties) but some is lost forever. You can't look at the mass/spin/charge of a black hole and somehow use that to figure out exactly what objects went into it and when those interactions happened.
And that's where the paradox lies - every other object in physics, if you could theoretically reverse time you can figure out exactly what objects interacted with it and when, but for a black hole you can't.
