A successful shot will take out a chunk of health from you, or your enemy's, hit point pool. Depending on your settings, the HP pool for enemy and allied tanks is represented as a percentage or a remaining/total value. All of this can be adjusted in your Settings.
During battle, your own HP pool is shown in the lower left of the screen at the top of the vehicle status window. The status box also includes tiny icons representing all of the various modules and crewmen within your vehicle. These modules and crewmen, when damaged or destroyed, dramatically affect the performance of your vehicle.
Hit point damage and module/crew damage are distinct. Damaging a module only affects that module, but not necessarily the hit points of the tank, and vice versa. However, the same shell can damage both HP and modules, or armor and crew, since it travels through the tank after penetrating the hull.
Just like vehicles, modules and crew have a hit point pool. These are displayed as one of three color states in the status window in the bottom left corner of the screen.
Default (no color shading): Enough hit points for module and crew to be fully operational.
Yellow: This state signifies that a module has taken considerable damage but is still operational. Tracks remain fully operational in this state, whereas every other module works at 50% efficiency. Crew members have no yellow state.
Red: This state signifies that a module is inoperative or that a crew member is knocked out. Crew members remain in this state unless a First Aid Kit consumable is used to restore them to full health, whereas modules will automatically be repaired over time by your crew up to the "Yellow" state.
All module and crew state changes are accompanied by a voice message.
Crew Knocked Out
As soon as all crew members are knocked out, the tank becomes inoperable. Consumables, like First Aid Kits, cannot be applied anymore at this point; there's no way to restore the tank to operating condition. It counts as destroyed, even though its hull stays on the battlefield with all its remaining hit points.
Ammunition Rack Explosion
If the ammunition rack's hit points reach zero, it explodes, destroying the tank and its crew completely, regardless of the remaining hit points on either of them. The only case where the tank does not explode with a "red" ammo rack, is when the rack is empty.
There are two ways the enemy can set your tank on fire.
If your fuel tank's hit points reach zero, your tank automatically catches fire.
Each time your engine gets hit, there is a chance that your tank catches fire. Note that the transmission counts as part of the engine and can be situated well apart from the main engine compartment.
While your tank is on fire, it constantly takes HP, module, and crew damage. The exact damage rate depends on the tank. Fires will naturally be extinguished (though sometimes not before your tank is destroyed!), but can be put out immediately by using a Fire Extinguisher consumable.