If you look at the various skills in the talent trees of each character, you'll see that some cause opponents to be Disorientated, Brittle, or Staggered (I think - can't recall exact names at the moment). You'll also see other skills that cause massive amounts of damage (usually 400-600%) when the enemy is in one of those states.
The trick is, one class can cause each of these states, but only the other two can cause more damage when the enemy is in that state. A cross class combo is taking advantage of this.
I found the easiest way to do this is to add tactics for each character to take advantage of this. Set the trigger to an enemy being in this state, and the action will be the character's skill that takes advantage of this. This way you'll get the damage bonus for free (assuming you aren't controlling the character in question, of course).