In military terms: the concept of establishing a greater volume of effective fire than your enemy. This is the objective of nearly all tactics, technology, and methodology in combat.
The basic idea of fire superiority includes the idea of 'effective' fire. The volume of effective fire includes both the concepts of the number of rounds fired and the accuracy with which they are fired. A unit which fires 1000 rounds with an effective 10% accuracy establishes a lesser volume of effective fire then a unit that fires 500 rounds with an effective 50% accuracy. This is one of the main reasons the United States Marine Corps emphasizes training Marines to fire accurately over both long and short ranges.
Also important is the concept of fire support, or the use of resources located outside of the immediate field of battle. Such resources include artillery, which ranges from 60mm mortars to 155mm artillery; air support, such as A-10 Warthogs or AH-64 Apache helicopters; and reinforcement or resupply. The first two have a direct effect on the enemy, killing soldiers and destroying equipment. The last mostly contributes to the original volume of effective fire. These are especially important in the United States Military, where the availability of powerful and accurate artillery, a dominant air presence, and mobile and plentiful reinforcements and resupply can often make up for deficiencies in numbers.
Finally, terrain and emplaced defenses can make up for deficiencies in numbers or other weaknesses. A prepared position atop a strategic location can allow a defending force to minimize its numerical disadvantage to a great degree. An ambush position allows a force to maximize the value of its soldiers, giving each the opportunity to account for a greater volume of effective fire then would be expected during standard combat.
The reason this concept is so important is that it just about guarantees victory in a given situation. When fire superiority is established, it means the enemy is losing fighting capability faster then your side. Not only are his soldiers being killed faster, but he is being forced to take cover to maintain what effectiveness he retains, which means your casualties decrease. His capabilites decrease at a greater rate then yours. In the long run, fire superiority guarantees continued fire superiority, which invariably leads to an enemy's eventual destruction.
A point has been brought up regarding situations wherein the goal of an engagement is not the destruction of an enemy force. It is true that not all of these situations require the establishment of fire superiority to be effective; however, for the vast majority of combat operations, the intention involved causing the maximum damage to the enemy possible. Even covert units, whose goal is to avoid detection, design encounters in such a way as to allow them to, if confronted, quickly establish fire superiority for as long as it takes to withdraw. The concept of maneuver is intertwined with that of fire superiority; almost all maneuver is designed to place a unit in a position to maximize its effectiveness, or to place the enemy in a position to minimize his effectiveness. Again, it almost all comes down to fire superiority in a given situation.
It is fire superiority that makes or breaks a given engagement. A force that can quickly attain fire superiority, then follow through until the enemy's destruction- such as the Marines- or disengage before the enemy can react- such as the Navy SEALS can be victorious in almost any situation.