Cavalry (or horsemen) were soldiers or warriors who fought mounted on horseback. Cavalry were historically the third oldest (after infantry and chariotry) and the most mobile of the combat arms.
The designation of cavalry was not usually given to any military force that used other animals, such as camels or mules. Infantry who moved on horseback, but dismounted to fight on foot, were known in the 17th and early 18th centuries as dragoons, a class of mounted infantry which later evolved into cavalry proper while retaining their historic title.
A man fighting from horseback also had the advantages of greater height, speed, and inertial mass over an opponent on foot. Another element of horse mounted warfare is the psychological impact a mounted soldier can inflict on an opponent.
The mobility and shock value of the cavalry was greatly appreciated and exploited in armed forces in the Ancient and Middle Ages; some forces were mostly cavalry, particularly in nomadic societies of Asia, notably the Mongol armies. In Europe cavalry became increasingly armored (heavy), and eventually became known for the mounted knights. During the 17th century cavalry in Europe lost most of its armor, ineffective against the muskets and cannon which were coming into use, and by the mid-19th century armor had mainly fallen into disuse, with some regiments retained a small thickened cuirass that offered protection against lances and sabres and some protection against shot.
In battle Cavalry had a great advantage over the common foot soldier. The speed, mobility, height and force of impact allowed by the horse allowed the horseman a great advantage over a soldier on foot. Mounted troops carrying projectile weapons also had the ability to harass enemy armies. This tactic has been used since ancient times. The Huns, Scythians, Parthians (also known as Arsacid), Carthaginians, Celts, all renowned horsemen of the ancient world, used this to great affect against powerful enemies like Rome. Another universal use of cavalry since ancient times was their role as scouts and reconnaissance groups. The speed and mobility of light cavalry made them ideal scouts and even civilizations that did not use a comparatively notable amount of cavalry, like the Romans or the Chinese, used them as scouts.
Throughout history cavalry has been an integral part of most nomadic cultures, especially the aggressive civilizations that raided and pillaged other civilizations to acquire resources. People like the Mongols, Huns, Russian Cossacks, Indian Marathas, Arab Bedouins, some Native American people such as the Comanche, Sioux, Lakota etc became well known horsemen since use of cavalry greatly complemented their lifestyle.
When speaking of heavy cavalry, warriors using spears or swords could rush enemy foot soldiers and quickly crush disorganized enemy units, Alexander the Great used this tactic to great affect in his conquest, using an "Hammer and Anvil" approach. The medieval knights were mounted "shock troopers" of their time, they crushed through enemy flanks using heavy weapons (mostly melee weapons) while protected by their heavy armor.
In the ancient world and Middle Ages, the speed and mobility of light cavalry allowed the use of various effective combat tactics. Mounted archers were ideal for "hit and run" tactics, a tactic commonly used by Native American warriors from the colonial age to the early 20th century. This tactic was also used by Indian horsemen, specially the Marathas.
Mounted archers used the speed and maneuverability of their horses to use the "parthian shot" tactics which involved shooting arrows or a gun at an enemy while pretending to retreat or run away from them. As the enemy is in pursuit, they would be constantly hit by arrows while being unable to use their melee weapons until they got close enough. First developed by Parthians, this tactic was used by Huns, Mongols, Seljuk Turks and Native Americans as their light horsemen had accurate archery skills and were faster than most other horsemen at their times. The Saracens also used this tactic against heavily armored European knights during the Crusades.
Use of parthian shot eventually leads to the "feigned retreat" tactic. This involved using a small force to agitate the entire enemy army and then retreating, keeping them focused on trying to pursue the attackers by constantly launching hit-and-run attacks and denying them the opportunity for a battle and ultimately luring the disorganized, tired and blindly determined enemy away from their fortified positions and into an ambush by the larger portion of the force. According to the Mongol Expert Timothy May, Ph.D - "the Mongols are all about the feigned retreat". Even after the end of the Mongol reign, former Mongol occupied lands such as Persia or Eastern Europe used good amount of cavalry in their armies.
Cavalry played a key role during the colonial period, specially during the colonization of the Americas. Many natives were not familiar with cavalry and didn't know how to counter them. Small European forces easily managed to take down thousands of native warriors using their cavalry.
After the widespread adoption of gunpowder, armor started to lose it's merit on battlefields, specially European battlefields. Then the melee cavalry mostly became lightly armored hussars, who carried light weapons (such as the cavalry sabre) and were used to mount surprise attacks and quick flanking attacks on the enemy. This tactic became surprisingly useful when properly utilized in co ordination with battlefield conditions - for example, a surprising cavalry charge using the cover of a fog could change the course of a battle. This tactic was efficiently used by Napoleon. Cavalry raids were also used to cut off enemy supplies.
Mounted dragoons (mounted soldier armed with a musket or blunderbuss) were another addition to European cavalry during this time. The carried lighter weapons compared to standard musketeers, but combined the mobility of horses with the range and power of their firearms.
Use of cavalry in direct combat started to slowly decline after widespread adoption of early modern firearms like the repeating rifle as use of infantry became more efficient cost-wise. Then the cavalry were primarily used as scouts and reconnaissance groups. Melee cavalry like the hussars and lancers slowly got disbanded. US cavalry served as scouts, raiders and as mounted infantry throughout the American Civil War and the Indian Wars. Armies also started using horses for fast transportation of infantry units while outside battlefield. However bandit groups like Jesse James and/or guerrilla groups like the Villistas (Mexican revolutionaries lead by Pancho Villa), Native Americans like the Comanche, Lakota, Sioux used horses to make lightning raids. It is known that later armies also used cavalry charges while being assisted by rapid firing weapons such as the Gatling gun in tactics like the "suppress and slaughter" tactic. But while such tactics were fast and had high shock value, they had a high chance of turning out to be suicidal at times.
Cavalry also found new success with European superpowers in Imperial operations (irregular warfare), where modern weapons were lacking and the slow moving infantry-artillery train or fixed fortifications were often ineffective against native insurgents. The British Indian Army maintained about forty regiments of cavalry, officered by British and manned by Indian sowars (cavalrymen). Some modern Indian and Pakistani Army regiments can track back their lineage to these famous regiments. The French Army maintained substantial cavalry forces in Algeria and Morocco from 1830 until the Second World War.
After World War 1, thanks to the arrival of weapons with a high rate of fire, cavalry units became inefficient to use in normal warfare, and so were usually kept as a scouting role when against enemies with machine guns. As countries became more and more modern, cavalry was eventually replaced with vehicles.
The advantages of Cavalry are clear. The horse allowed for a mounted warrior to quickly move around the battle field, hit fast and hard, and allow them to tower over enemies. This was especially an advantage when crossing rivers, when Hannibal first entered Italy, his horseman were able to attack an Roman army crossing a river and because the horseman were elevated above the river, they stayed dry and avoid fighting the current.
Despite the advantages of horsemen there were a number of draw back to cavalry. One of the biggest issues was the use of spears and pikes in an organized fashion. The Greek phalanxes is one such example of this, because of the multiple rows of spear horsemen and there mounts would impale themselves in a frontal charge, so attacking the flanks and rear was preferable. English longbowmen would hammer wooden stakes into the ground to stop charging knights. Additionally horses can be scared fairly easily by unknown animals such as elephants or camels due to their "odd" appearance and smell. The Mongols and Turks faced this problem against elephants during their early invasions of India, the European armies faced similar problem when they faced camels of the Saracens during the Crusades. However horses that are trained around these animals would not panic, making it easier for the camel or elephant using army to use their own cavalry. Another key disadvantage of cavalry was it's high upkeep and maintenance cost. So some empires that needed to field a vast army over a densely populated land preferred infantry (specially gunpowder armed infantry) over cavalry. Specially the Chinese, Ottoman, Mughal empire faced this problem.
In the show the first warrior to be seen on Horseback was the Knight, however this was only in the final fight and was likely not a tested factor. The first official use of proper cavalry, was in Alexander the Great vs. Attila the Hun. After this episode Mongol vs Comanche featured mounted horse warriors as well. In the third season features the most mounted warriors to date, however it mostly the commander who is seem on horse back while his soldiers fight on foot.