What does the X mean over my crosshair in BF3?

Solution 1:

It means that you have hit the enemy. This is especially important when firing rockets at enemy vehicles, since frequently after you fire you have to hide to avoid dying so you can't see if you got a hit.

It does not mean, however, that you have disabled or destroyed a vehicle, so also be alert for the "vehicle disabled" and "vehicle destroyed" notifications coming up on your screen