Light cavalry was used to scout, provide defensive screening and engage in skirmishes, as well as pursuing fleeing enemies and carrying messages. They used lighter, faster horses which were not armored, and wore little to no armor themselves. Light cavalry troops were archers, but they often carried other weapons as well, from swords and daggers to maces and poleaxes.
One of the Parthian's favorite tactics was to have the light cavalry ride in on an army, raining down arrows. They would then pretend to retreat and the enemy would follow. The Parthian horsearchers would turn around and fire arrows at their pursuers. This technique came to be called the "Parthian shot." In some cultures (Samaritan, Scythian) women were common among the light cavalry and archers. The tattooed Scythian women were particularly noted for their status as warriors.
Later, in 15th century Hungary, light cavalry troops were also used to infiltrate behind enemy lines, capture supply trains and hold or destroy important intersections or roads. As the weaponry of the time changed, the light cavalry went from archers to riflemen. Under Napoleon, the light cavalry was organized into small units that could easily be broken down into smaller units for use as pickets and scouts. The light cavalry often rode at the forefront of the army and along its flanks, acting as scouts to make sure that the main body of their army was not surprised.
In the Middle Ages it was a common for knights to fight by using their horses to gain position on the field and then send their horses away while they fought on foot. This was especially done when the heavy cavalry's charge was rendered ineffective by the terrain. However, the heavy armor had to be lightened to allow for this flexibility, and thus the medium cavalry or "mounted infantry."
The ability to fight both while mounted and while on foot offered advantages in mobility and versatility. Though armored, the soldiers could still move freely and they had their horses to help them get inside the enemy's ranks. Fully armored heavy cavalry began to disappear as guns became more common on the battlefield and the more lightly armed and flexible medium cavalry rose to prominence in Europe and America.
Leading us to the Dragoons of the 18th century. These medium cavalry troops fought with pistols in addition to sabers. They were trained with the sword and were capable of fighting from horseback, or on foot.
For Further Reading:
Cataphracts and Clibanarii of the Ancient World
Cavalry Weapons and Organization
Hungarian Renaissance Warfare
Cavalry Tactics and Combat during the Napoleonic Wars
Dragoon Soldier - Historical Background
Interestingly, while researching cavalry, I was most reminded of the character of Beka Cavish from Lynn Flewelling's Nightrunner books. Beka and her fellows are a great example of light cavalry. What are you favorite examples of the use of cavalry in fiction?