The Field of Fire was the pivotal battle that decided the result of the War of Conquest. To face the invading Aegon the Conqueror in open battle, Kings Mern Gardener of the Reach and Loren Lannister of the Rock combined the armies of both the richest Kingdom and the most populous Kingdom. Their total force numbered 60,000 men. In contrast, Aegon's army was outnumbered five to one, most of whom were conscripts from previous conquests. The battle was fought on a wide field in the Reach.
However, Aegon the Conqueror unleashed his three dragons against the enemy army. Four thousand men burned alive that day, including King Mern himself. King Loren, instead, bent the knee to the Targaryen warlord. He was thus appointed Lord Paramount of the Westerlands and Warden of the West
With the death of King Mern, House Gardener, which had ruled the Reach since the time of the First Men, became extinct. House Tyrell, the hereditary stewards of the Gardeners, then surrendered Highgarden to Aegon. In return, Aegon raised Harlen Tyrell, the head of the family, to Lord Paramount of the Reach and Warden of the South. This would forever aggravate House Florent, a cadet branch of House Gardener that felt the Tyrells' claim was weaker than their own, because the Tyrells only descended from House Gardener through the female line. However, it was House Tyrell that surrendered Highgarden to the Targaryens, thus it was the Tyrells that began to rule the Reach under them.
In the books
In the A Song of Ice and Fire novels, a combined Westerlands-Reach army of 60,000 well-equipped soldiers faced Aegon Targaryen's much smaller army of only 10,000 men. Aegon's initial invasion force only numbered 3,000 soldiers, but grew to 8,000 when the Riverlords rebelled against the ironborn to join the Targaryens. Further levies were then taken from the defeated ironborn and Stormlords, bringing the size of Aegon's army up to 10,000. The ironborn and Stormlords had suffered heavy losses from the dragons, probably explaining why they didn't contribute as many troops as the Riverlords (that, and the Riverlords had willingly joined the Targaryens), and this also may have been offset by earlier losses in the campaigns. Thus Aegon was outnumbered over five to one, and some of his men were conscripts of dubious loyalty from the Stormlands and Iron Islands.
The separate Targaryen armies linked up at Stoney Sept and marched south, meeting the combined Westerlands-Reach army at a plain somewhere in the northern Reach. For the first and only time, Aegon risked fielding all three Targaryen dragons at once. Because Aegon and both of his sisters would be in the air atop their dragons he needed to appoint a separate commander for his land army, so he named Jon Mooton of Maidenpool, one of the first lords to come over to his side once he landed in Westeros.
As the two armies met, the dragons set fire to the dry grass, causing chaos and confusion in the larger army. The dragons burned 4,000 men alive, including Mern IX Gardener, leaving the Reach forces leaderless. Another 10,000 men were so badly burned that they were unable to fight. Aegon's smaller army attacked the panicking larger host, killing hundreds more, and the remaining ~30,000 men surrendered. In the entire battle, the Targaryens lost barely 100 soldiers. Visenya Targaryen took an arrow to the shoulder but recovered.
While an exact location for the battle has not been provided, it can be narrowed down with reasonable accuracy. It is stated that it took place on a broad flat plain in the lands south of the Blackwater River, in the Reach, near to where the Goldroad would later run. Further to the east, the Goldroad actually crosses over to the north side of the Blackwater, so the battle had to have taken place further west. This matches with the description that the Targaryen army advanced south from Stoney Sept, which is located on the Blackwater - the Goldroad is south of Stoney Sept.