The term counter-battery fire refers to the concept of detecting the source of artillery (shells or rockets) landing on friendly forces and firing back at them with artillery, suppressing or destroying them in order to protect the friendly forces and reduce enemy artillery strength.
Originally, counter-battery fire relied on ground or air-based artillery observers noticing the source of the artillery fire (due to muzzle flashes, smoke, spotting the artillery pieces, etc.) and estimating firing solutions to strike back at them. Artillery spotting, along with reconnaisance, was one of the earlier roles for aircraft in warfare (see World War I). Modern counter-battery fire relies on counter-battery radars, which are able to calculate the source of incoming artillery shells very accurately and quickly. So quickly, in fact, that return fire can sometimes begin before the first enemy shell has landed.
The development of accurate and fast counter-battery fire lead to the concent of shoot-and-scoot and concentration on the development of highly mobile artillery pieces (typically self-propelled guns like the US M109 Paladin or Soviet 2S1, or vehicles with mounted rocket launchers like the US M270 MLRS or Soviet Katyusha). The idea is to fire and then move before any counter-battery fire can land on the original position.
The task of destroying enemy artillery batteries can also fall to attack aircraft, but unless they are already on patrol overhead, it is usually not quick enough to save friendly forces from damage. More usually, ground-based counter-battery fire would suppress the enemy battery/batteries and force them to move, while aircraft would follow up later with a strike to destroy the rest of the enemy artillery.
See also: Artillery (Counter-battery fire)