Heavy cavalry is a term used by military historians to talk about mounted shock troops of the pre-gunpowder period. Although the exact details of equipment varied from nation to nation and culture to culture, the heavy cavalry was typically heavily armored and made use of melee-style weapons, including but not limited to lance, sword, spear, and mace. The horse might also be armored, although not in every case.
The major advantage of heavy cavalry is its speed. Because its range is limited, the primary uses were in pursuit, reconnaisance, and charge. During the medieval period, in fact, cavalry was almost always used as the primary variery of shock troop, usually in relatively simple frontal charges when battle was eventually engaged.
Of course, one of the best tactical uses of heavy infantry was their ability to circle or envelop their enemy in order to engage the unprepared rear. Although this tactic was not always used, since it required the somewhat unusual practice of keeping troops in reserve from the main battle, if the superior mobility of the mounted shock troops was used in this way, it greatly enhanced their effectiveness.
In fact, its primacy in the medieval period is somewhat surprising, considering the many limitations of heavy cavalry. Because of the enormous weight of the armor on both the horse and the rider, stamina was relatively low, so they could only be deployed effectively in short bursts. Additionally, they had virtually no value when stationary, since they were deprived of their main advantage, mobility. Heavy cavalry was also virtually useless in assaulting a fortified position, since horses have so much trouble in negotiating terrain other than flat ground. The superior stability of heavy infantry type troops, whose feet were on the ground rather than trying to balance on a moving horse (a problem especially difficult to overcome in the era before the stirrup), allowed them to use their weapons more effectively against stationary heavy cavalry and thus usually defeat them in relatively equal combat. Light cavalry, who could move and shoot arrows or throw javelins or other projectiles at the same time (even in retreat among the most skillful riders), could effectively elude the short-range heavy cavalry while still attacking. Thus, the only type of enemy against whom the heavy cavalry was particularly effective was the light infantry. The heavy cavalry could attack light infantry very effectively because they could easily neutralize the light infantry's main advantage, namely their long-range attack, by way of their superior speed. When the distance had been closed, the heavy cavalry had little to no trouble at cutting down the lightly armored infantry.
In an economic sense, the heavy cavalry signified an enormous investment by its supporting state. Other than the obviously expensive armor and fine horse that effective heavy cavalry requires, there is also the extensive training necessary not only to ride the horse and hit people with a weapon, but also the ability to do both at the same time. Some historians have estimated that about twelve productive civilians were necessary to support one medieval heavy cavalryman, and that's just in the most productive nations, like France. In less fertile areas, like the dry Middle East or mountainous Greece, heavy cavalry required immense state organization to provide the resources necessary to deploy them.
Given the many limitations of heavy cavalry versus the relatively specialized uses of them, one can't help but ask why they were used so extensively in the western world for so long during the medieval period. Although the Franks, who came to dominate much of Europe immediately after the collapse of the Roman empire, had used mounted troops fairly effectively ever since the Romans first encountered them in battle and wrote about them, I favor another explanation for this phenomenon. Rather, the professional soldiers of the day (and hence the military leaders) were usually mounted as a form of conspicuous consumption. As previously stated, the heavy cavalry requires a significant investment, so when a soldier is personally responsible for his own equipment, he's likely to take his social class disproportionately into account when choosing it. Thus, the adoption of a heavy cavalry fighting style in much of Western Europe was probably a way for the professional soldiery, who were also the lords and other societal elites, to show off their status within society. Mind you, that's just what i think given the facts that I have, and I haven't researched this as extensively as some.
All facts in this article and most interpretations, except where explicitly stated otherwise, come from Archer Jones's fine and extremely informative book, The Art of War in the Western World.