Accuracy

Accuracy is an indication of the precision of your weapon. It defines how straight your bullets will come out of the barrel of your weapon.

Firing Cone
Whenever a weapon is fired, any weapon, it never comes out of the barrel straight. They will deviate from straight forward by any given angle. As a general rule though, all the bullets will stay withing a cone. It is the angle of this cone that describes your weapon's accuracy.

There is a direct correlation between your accuracy percentage and the cone's angle. A weapon who's accuracy is 0% will have bullets coming out of the barrel up to an angle of 45° (forming a 90° cone in front of your gun). A weapon with 100% accuracy will always shoot its bullets perfectly straight. Basically, the cone's angle is approximately 100%-accuracy% (then multiplied by 90°/100%, to convert from percent to degrees).

For a better idea of how precise your gun is, you should concentrate on how far away your accuracy is from 100%. For example, a Sniper Rifle with 98% accuracy (firing cone of 4°) will actually be twice as precise as a sniper rifle with 96% accuracy (firing cone of 8°).

This bears repeating: a 98% accuracy Sniper Rifle is TWICE as precise as a 96% accuracy Sniper Rifle.

With that in mind, it also means that a weapon with 50% accuracy isn't much more precise than a weapon with 25% accuracy.

Don't be fooled by the numbers.

Accuracy boosts
When you are granted an accuracy boost, your accuracy percentage is not actually increased by that amount. Rather, your firing cone will be reduced by that much. So if a Machine Gun with 70% accuracy has a +50% accuracy bonus from proficiency, the actual final accuracy rate will be 80%. While this may sound like less of a bonus you you might have thought, remember that the firing cone of a 70% accuracy weapon is 50% bigger than the 80% one, so much less precise.

NewFiringCone = OldFiringCone/(1+AccuracyBoost)

Weapon Recoil
Recoil is an effect that reduces your accuracy as you fire. To reduce this effect, either find a weapon with reduced recoil, or fire in short bursts.

Weapon Sway
Weapon sway is the fact that your weapon will not be perfectly still when you aim it. This effect is most visible with Sniper Rifles. The effect goes away if you hold still for a little while, and will go away faster if you are crouching.

Scope
When weapons are equipped with scope, there is a light red circle in the middle of your scope that represents your (static) firing cone. This circle is known as the "Shot Deviation Ring". Unlike your cross hair, the ring will not increase in size when you are running or firing, even though your accuracy will actually be reduced. This circle is accurate only if you currently don't have any recoil or sway penalty.

Because this ring represents you firing cone, a weapon with more zoom will have a bigger circle, but that doesn't mean it is less accurate. Since everything will look bigger on screen, the final result will be the same.

With Sniper Rifles, if you are aiming for a Head Shot, make sure the head is at least as big your scope circle. If the head is any smaller, your bullet will probably miss the target entirely, and tip the enemies to your location. Under these conditions, you are better off just aiming for a body shot.

Disclaimer
The above numbers, percentages and degrees are all original research with no code to back them up. They are however, a pretty good indication of reality (relative to Borderlands), and should be a rule of thumb to follow.