Penetration is the value that determines the chance of penetrating enemy armor. Whether a shot penetrates or not is very important in a fight. It can mean the difference between a smouldering wreck or a lucky escape. If a shell penetrates, full damage of that particular vehicle is applied. If it doesn't, the shell will (in most cases) harmlessly bounce off.
The formula that company of heroes 2 utilises is very simple:
penetration/armor x 100
This is the chance of penetrating enemy armor. Unlike company of heroes though, vehicles do not have side armor. Instead, front armor is the first half of the vehicle and rear armor the second half of the vehicle. Veterancy of some vehicles increase armor values or penetration values.
A SU-85 tank destroyer encounters a panther. A shot is fired, and the front armor of the panther is hit. What are the chances of penetration? The SU-85 has a penetration value of 170, the panther a front armor value of 270.
170/270 x 100 = 63%
If it does penetrate, 160 damage will be applied to the panther.