The Battle of the Trident was the climactic battle of the civil war known as Robert's Rebellion.
Prince Rhaegar Targaryen was slain by Lord Robert Baratheon during the battle, resulting in a crucial and critical victory for the rebel forces. Rhaegar was killed at a ford in the river from a swing by Robert's warhammer. Smashing the rubies from Rhaegar's armor with his killing stroke led to the site becoming known as the Ruby Ford.
Robert was injured in the battle, but he sent his personal Maester to treat the injuries of Barristan Selmy, recognizing the knight's courage and loyalty despite being on the enemy side. Unable to ride, Robert sent his most trusted ally, Lord Eddard Stark, south to secure the capital. Lord Eddard, however, arrived to find the city already sacked by Lannister forces as a show of fealty to the rebellion.
The defeat marked the beginning of the end for the Targaryen dynasty. No army stood between the rebels and King's Landing, the only other royalist armies being Mace Tyrell's army besieging Storm's End and Tywin Lannister's marching from Casterly Rock towards the capital. Since Robert was wounded in the battle, it fell to Eddard to lead the rebel army south towards King's Landing, hoping to arrive before the Lannister reinforcements.
Ser Barristan was close to death when he was brought before Robert. Though he was counseled to kill him, Robert spared his life, and even sent his own maester to tend to his wounds.
In the books
In the A Song of Ice and Fire novels, the Battle of the Trident took place at a ford over the River Trident several hundred miles north of King's Landing. The battle was only possible due to some impressive maneuvering by Lord Robert's army from the Stormlands, which had to travel through hundreds of miles of enemy territory to link up with the Stark, Tully and Arryn forces north of the river.
The battle itself was on a large scale, with Prince Rhaegar leading 40,000 royalist troops. The rebels had slightly less, but the rebels were more experienced due to almost a year of warfare beforehand. The battle was quite bloody with high casualties on both sides, but in the end it was the royalist force which broke and ran after Prince Rhaegar's death by the hands of Robert Baratheon. After Prince Rhaegar was killed, men on both sides stole the rubies that bejewelled his armor and crown.
Other notable characters present at the battle included Lord Jon Arryn, Lord Hoster Tully, and Lord Roose Bolton. The latter, following the rebel victory, suggested to have Ser Barristan Selmy executed.