The Critical Hit ability is both offensive (anytime you attack in GE, GBG, Hood, or quest map,) and defensive for your city units, but only triggers between units from the same age.

Critical Hit is an ability granted by the GB Arctic Orangery aka Snowflake, and is a completely separate bonus from your attack boosts gained by Aachen, CDM, Zeus, checkmate squares, CE and above barracks, etc.

When you are in the battle screen if you hover over enemy units you see a range of possible damage you can do; this already includes terrain bonus, your attack bonus and the enemy defense bonus. For example, if you move to a more favorable terrain for your attacking unit, you will notice your attack possibility on enemy units go up from say 4-6 to maybe 5-7. Likewise, if you are fighting someone with high defense boost, a unit that would normally do 6-8 damage against a certain kind of enemy will show a lesser possible damage range more like 4-5. So all the complex calculation of the attack, defense and terrain boosts is figured into the damage you can do in one hit.

The Critical hit bonus of 150% is applied AFTER that, when you actually attack its like a roll of the dice, if the possible range is 4-6, you could do either 4, 5 or 6 damage. If you roll the 6 damage and trigger the Critical Hit (the chance of triggering it increases with each level of the GB) you would do 9 damage instead. If you have a possible damage range of 7 or above when attacking something and trigger the Critical Hit, the enemy is going to die in one hit.

Arctic Orangery Critical Hit ability also works with your city defending army, but still will only trigger against units from the same era! For example, if you have Colonial defending units and someone attacks your city with Industrial units, you will not see a critical hit, but if you are attacked by Colonial troops, it could trigger critical hits when your Colonial units defend.

The Critical Hit ability from Cosmic Catalyst (SASH Great Building) works the same way and stacks with the AO's critical hit described above.  But it will never be as cool-looking as the AO, which is maybe the coolest looking GB in the game.