So the suppression rules are as follows, when you shoot an enemy target, you not only have a chance of hurting but you also reduce their morale by a 1 - 15 points (I think). Then any unit that was adjacent to the one you were shooting at also suffers a slightly smaller morale penalty. Finally any unit within a 2 tile radius of the original target suffers a smaller penalty. This means that shooting an enemy has a negative impact on their morale even if you don't hit them. Now when a target gets morale of zero, their indicator turns yellow and they become panicked. While panicked, they can't perform any special abilities but can move / shoot. The thing is that morale itself is very important to fighting ability. The way it works is that morale ranges from 0 to 100. If your morale is above 60, you get +1 attack skill for each point it exceeds 60. If your morale is below 40, you suffer a -1 attack skill penalty for each point below 40. So a unit with morale 30 suffers -10 attack skill while a unit with morale 80 enjoys a +20 attack skill bonus. Attack skill is one of main things that determine whether you hit or not. Therefore, once you do enough to reduce enemy morale, they become much less effective. Morale is reduced by attacks (see suppression above) but also by things like seeing an ally get killed, killing an enemy, seeing an enemy die, seeing reinforcements arrive, seeing more enemy patrols arrive, losing health, gaining health, etc. So morale is very important because it directly affects your soldiers fighting ability and that of your enemy. Your team are elites so typically start the battle with high morale so will have an advantage at first but that advantage will quickly evaporate if things go badly. Similarly, weak enemies will fight much better if they are emboldened by the arrival of allies or something.