Some units in the game have armor. Armor does just what you might think - it protects the armored unit from enemy fire. The most obvious example of an armored unit in Spring:1944 is a tank, and you can't hurt a tank by throwing rocks at it. Makes sence so far, right? Good, it's gonna get worse.
To damage something with armor, you have to penetrate it either by having a fast and heavy bullet, or by a big explosion. Fortunatly, usually you have access to at least one of these.
Armor in Spring:1944 is always directional, with front armor being the strongest and rear armor - the weakest (with some exceptions). It is good parctice to use the "turn" command to make units face the enemy with their best armor.
Anti armor weapons show their penetration when ordered to attack. Penetration decreases with distance for AT rounds, so if you have a weak anti-armor unit you can try moving in closer and take the risk.
In most situations, dedicated anti-armor weapons cannot target infantry. Even if they do hit infantry, there will be no explosion, as AT rounds do not explode. Smaller AT weapons can aim fast enough to be able to target infantry without much difficulty, but they become more like sniper rifles, then actual AT guns.
The deployable AT weapon you start out with is a great example of something that shoots AT rounds.
in the explosion department, everything is simple: the bigger the explosion, the more damage it will do. Explosions mostly ignore armor and will usually do similar damage to all armored targets. On the low range, the most common explosive weapon is the hand grenade. Tipical hand grenades will destroy most light tanks in a few hits. Even medium tanks are in serious danger if there is an extra squad of infantry around.
When it comes to bigger grenades, usually HE rounds come into play. Shot from tanks, assult guns and other exotic weaponry. they usually have medium or long ranges and, like grenades, mostly ignore any armor. Another similarity is the ability to attack infantry, usually resulting in many, many casualties. Since the effectivness of the rounds does not decrease with distance, these weapons are often used at maximum range.
Notable examples are the ISU-152 and infantry support variant of the Sherman.
A mix of AT and HE results in HEAT rounds. They do not loose their use with distance, are much cheaper than HE and are much more reliable in general. As a drawback they are not as powerfull in most cases. Most Italian armor has these in one form or another.