(Split into two posts due to length. I'll cover light and medium cavalry next Friday and put a link in this post.)
The first cavalry troops date back to the Parthian army around the 6th century BC. It seems to have sprung up first among the nomadic cultures who spent much of their time on horseback, such as the Scythians. It is after the 6th century that cavalry troops began to replace chariots, although the change didn't come overnight. The Parthians used two types, with which you're probably at least a little familiar: light cavalry and heavy cavalry. Medium cavalry came into use later and was often used as mounted infantry. Throughout the ages and between cultures, the purpose of these troops has been much the same, offering similar advantages and disadvantages.
Even from Parthian times the heavy cavalry was heavily armored. The Parthian cataphracts were armored from head to toe in metal scales or plates and supplemented with chain. The horses, too, were armored. Some completely covered in armor like their riders, while others were only armored over the front parts of their bodies.
The cataphracts were the Parthian's answer to the hoplites and the phalanx formation. Because troops locked their shields when they were fired upon, they were left open to assault. The cataphracts would ride in, forcing them to break formation and picking them off with a long lance called konto. Our image of the classical medieval knight actually has ancient roots.
In terms of weapons, the heavy cavalry troops often wielded two-handed lances, without shields. They also often carried swords, maces or axes and some wielded one-handed lances so that they could also carry a shield.
One of the main differences between the medieval heavy cavalry and the ancient heavy cavalry was actually the stirrup. The cataphracts didn't have them, and so they were a lot less balanced and secure when it came to melee battle. They avoided it whenever possible because their heavy armor made them an easy target if they were knocked from their horse.
The heavy cavalry, of all eras but especially in Parthian times, needed two things: level ground and archers. The archers forced the infantry to shield themselves or scatter, and without archers the cataphracts became much less effective. And, because they were so heavy, they needed flat ground to build up the momentum of the charge. Because of this generals about to engage heavy cavalry sought inclined ground, the upward charge rendering the heavy cavalry less effective or entirely useless.
The armor used by heavy cavalry was expensive and required frequent maintenance, and like the medieval knights, the ancient heavy cavalry troops were often the upper classes of their societies. They would be required to provide their own horses, weapons and armor. In contrast, in Napoleonic France, the lancers of the heavy cavalry were largely green troops, mounted on horses that were lacking in training, but led by a very experienced and skilled senior officer.
Against the Parthian cataphracts, the Romans often ordered their own, lighter cavalry not to engage directly, leading the cataphracts to chase them about and tiring both the soldiers and the horses that had to carry such heavy armor. Once they were tired, they were easier to defeat.
However, a cavalry charge at the right time could cause quite a lot of damage, and could even turn the battle. Heavy cavalry would often be held back until the right moment presented itself. Then they would charge. The effect wasn't just physical; the charge of heavy cavalry has a psychological component as well. Consider the difference in size between yourself and a large horse. Then imagine a tight line of them charging at you bearing metal-clad soldiers carrying sharp lances, while battle cries and the pounding of kettle drums filled the air. I know I'd wet myself.
The heavy cavalry were shock troops. Meant to ride down on a weakened army and smash them to bits.
Light & Medium Cavalry