It is not really that complicated, but it is kind of hard to explain. Lets assume you are in a typical U.S plane, with 6 .50 caliber machine guns mounted in the wings (3 in each wing). If your guns were not calibrated, they would all fire in a straight line. This means at any given range (be it 300 yards or 600 yards or anything else) your bullets will hit at about the spacing of your guns. So if your guns are 6 inches apart on each wing, you'll have 3 streams of bullets coming from one wing, then three streams of bullets coming from the other wing. This means you'll never really do any concentrated damage- if one set of guns is tearing up the fuselage of the enemy plane, the other set of guns is missing past one wing.
When you 'calibrate' the guns for a certain range, you are basically making it so the bullet streams cross a certain distance away from you. So if you have your calibration set to 400 yards, all 6 guns are sending forth a stream of bullets that crosses the path of the other guns at 400 yards. That way, if the enemy plane is 400 yards in front of you, you put your gunsight on his fuselage and you are hitting with 6 guns to the fuselage, instead of maybe 3 (or none) if you didn't have your guns calibrated.
Calibration isnt so important for nose mounted weapons, since they will always be hitting close together anyway, but it is critical for doing damage with wing mounted guns.