Effective Range refers to two parts of the same equation, as well as multiple variables, and of course the difference between theory and practice.
The first, (referring to weapons as opposed to ammunition) being MOA or minute of angle. The difference between good and poor accuracy is usually determined in a 1MOA group. 1 MOA is the measure of the angle, that is formed with as a triangle, with the muzzle as the top and the group as the base.
1 MOA is roughly equivalent to a 1 inch diameter group at 100 yards (91 meters), or to 2 inches at 200 yards, and so forth.
It can be figured then, that if rifle X shoots 1MOA groups, it means that at 300 yards this rifle could place roughly 5 rounds in a circle of no more than 3 inches in diameter. Modern sniper rifles, for example, when loaded with proper ammunition (which is the other facet of "effective range’’) could shoot 0.5MOA, or even 0.3MOA, which means 1 inch groups at 300 yards, or 2 inch (50 millimeter) groups at 600 yards (550 meters).
Ammunition is the other half of the equation. The load, the projectile (both design and material) and the condition of the rounds are what determines the right ammo for the job at hand.
For instance; If you are using a weapon for home defense, you want a round with low penetration, or even what’s known as a frangible round, which means that the moment it hits something, it begins to break apart, which curtails the velocity and weakens the energy, therefore decreasing the "effective range’’ of the round, and then obviously, the weapon.
Conversely, if you want to shoot, say, an Elk at 300 yards, you’d need a round that could not only travel that distance, but retain sufficient trajectory, as well as velocity to cause the greatest possible wound cavitation, and thus, the greatest possible injury.
The round, in order to do that, must spread out, rather than entering, and continuing on through without causing the cavitation necessary to damage and kill an animal the size of a full grown Bull Elk. The round best suited (depending on your experience) would be something along the lines of a 7mm 125grain round. It’s a moderately heavy round, that has minimal drop and is high velocity.
A round like the .223 (the current military workhorse) is a very efficient killing round, because of its’ tendency to tumble upon entering it’s target, causing extensive internal damage. What makes the .223 (M-16) problematic is the fact that the projectile itself is so light, that in environments such as heavy jungle, the round has poor penetration (as compared to the heavier 7.62x39 of the AK-47), therefore the overall effective range of the weapon is compromised because it cannot penetrate heavy jungle.
In short, the effective range, in theory, is a two part equation, consisting of the effectiveness of the round, and the precision of the weapon. In practice however, variables such as environmental conditions, physical obstacles, and the condition of the weapon and the round cause the effective range to vary wildly.