The first rule of Fight Information is: You do not talk about Fight Information.
Just kidding. The "Approx. Dmg Inflicted" is an estimate of how much damage each unit (attacker and defender) will take if they fight. You can also see an illustration of it in the flashing part of the units' health bars.
Obviously, if a unit is expected to take so much damage that its health drops to 0, then it's destroyed. I've found the estimate is usually, but not always, a good approximation of what happens in the actual fight.