When shooting a gun, a projectile can travel to any location within the player's reticle.
When a player shoots, his reticle will grow larger. As he continues to fire, his reticle will keep growing, making it tough to gage whether or not a shot will hit an enemy.
The higher a player's accuracy is, the rate at which the reticule increases size will slow, allowing him a better chance at successfully hitting the enemy.
In the case of Hunters, the effects of accuracy will basically allow him to be more sure that his shots travel where his reticle is pointing.
For gun-wielding Cabalists or Templars, higher accuracy will increase the weapon's lock-on capabilities, allowing them to shoot at farther distances and be more sure that their shots will hit.
For every point added to the accuracy attribute you gain 2% additional critical hit damage.
Improving accuracy also allows for better gear to be equipped. Guns often require players to have a high accuracy before they are able to wield them. Some armor also requires accuracy, but it is often an insubstantial amount.