Each point of Armor Class subtracts one from the damage opposing shots do. You could think of Armor Class as being stopping power, hardness, impact resistance, structural integrity, armor factor or absorption (all of these have been proposed as potential renames for "Armor Class"). In Combat, the effect of Armor Class can sometimes be seen as bullets pinging off your plane (or your enemies' planes). Trade planes often have a high Armor Class rating, making them frustrating to fight with Autocannons or small Machine Guns, as bullet after bullet bounces off your target.
To minimize this pinging off effect versus enemy planes, the most effective method may be to maximize the percentage chance that your gun will fire a Critical Hit by using a gun with a high "Crit Chance" (such as a Flak Tube) and/or a Gun Mod with a high "Crit Chance Modifier" (such as Explosive Rounds). This is because Critical Hits bypass the Armor Class of any plane.
You can also protect your plane against damage with Armor Class mods. Wood-Reinforced Hull mods improve your Armor Class by 5, preventing all non-crit damage by Autocannons, and Steet-Reinforced Hulls add 12 points of Armor Class, enough to protect against small Machine Guns as well. The two mods together form a potent defensive combo able to stop even large Machine Guns, but are almost worthless against Howitzers (because of their high Damage rating) and Flak Tubes (because of their high Crit Chance).