For I dipt into the future, far as human eye could see,
Saw the vision of the world, and all the wonder that would be;
Saw the heavens fill with commerce, Argosies of magic sails,
Pilots of the purple twilight, dropping down with costly bales;
Heard the heavens fill with shouting, and there rain'd a ghastly dew,
From the nations' airy navies grappling in the central blue.
From Locksley Hall
by Alfred Lord Tennyson, 1842*
Note: also see gunship for discussion of air support in general.
Air support is the modern practice of assisting troops on the ground through the application of aviation firepower. There is a variety of types of air support which differ on how close to friendly troops (and how responsive) the air assets are. At one end of this spectrum is Close Air Support (sometimes abbreviated CAS). On the other is interdiction, which is the application of air power to delay, disrupt or destroy threats approaching friendly troops before they can engage.
Modern air warfare began during World War One. Originally used entirely for scouting and reconnaissance, airplanes began to fight each other in the air, and to engage moored balloons and Zeppelins, and by the end of the war had begun to branch out into bombers, fighter/interceptors and scouts. While it is probably impossible to determine when the first air-to-ground action occurred, all combatants came away from that contest metaphorically rubbing their chins in thought. By the Spanish Civil War, the German Luftwaffe had begun fielding not only units but types of aircraft intended for use against close and time-sensitive ground targets - the most famous of which is the Junkers Ju 87 Stuka dive bomber.
Once World War Two was fully underway, even those combatants which had concentrated on defensive interceptor fleets (such as the RAF) realized that the typical anti-aircraft armament of fast fighters was also quite effective at (at least) scattering enemy troops and equipment, and destroying it in many cases. The RAF began to fly 'rhubarbs' (target of opportunity ground attack missions with fighters) through the Lowlands immediately following the Battle of Britain, disrupting transport links. Locomotives were a favorite target, as they were easily spotted, unable to really dodge, handily sensitive to sharp knocks, and (best of all) when destroyed, blocked the rail link until cleared. While this was not done in direct support of ground troops until the Normandy invasion, the technique was heavily used to slow and disrupt German reinforcement of the invasion area.
Fighters are not the only means of air support. During the breakout from Normandy, the Allies pressed strategic bombers into service to attempt to blast holes in the encircling German lines. The result, the opening moves of Operation Goodwood, succeeded in breaking frontline German resistance, marking a new technique in aviation ground support. Later, in Vietnam, Desert Storm and Afghanistan and Iraq, the U.S. Air Force went so far as to place strategic bombers (B-52Hs, usually) at the disposal of ground controllers to allow them to perform 'on the spot' missions in support of a fluid ground combat situation. At the same time, as the threat of an enormous tank war in Central Europe arose during the Cold War, both blocs began to spend resources on dedicated tactical air support units. The epitome of this pursuit, the A-10 Thunderbolt II and the Su-25 Frogfoot, were both designed entirely to destroy armored ground units.
Helicopters began to perform air support in the Vietnam era, with the UH-1 Iroquois gunship and the first dedicated helicopter attack craft the AH-1 Cobra. The Eastern Bloc swiftly produced a whole succession of gunships for use in Afghanistan. The U.S., driven by necessity in Vietnam, also introduced the concept of the fixed-wing gunship with the AC-47 and then the purpose-built AC-130 line of air support platforms.
* Many thanks to Kizor for reminding me of this particularly apropos passage after I posted the writeup!