- "Tactics mean doing what you can with what you have."
– Saul Alinsky
- "Strategy requires thought; tactics require observation."
– Max Euwe
For quite a long time war was a simple affair: amass as many men as you can, arm them as heavily as you can, then hurl that snarling mass of sharp things and yelling bearded madmen at the enemy yelling bearded madmen.
But somewhere along the way someone figured out they can do better. That hitting a weakened enemy line with cavalry in the right moment will cause the men there to disperse, which will wreak havoc in the enemy morale, which will cause their entire army to abandon the battle. And so military tactics was born.
The long-term implications of tactics on the battlefield are, of course, enormous; but its immediate benefit is the recognition of the cavalry as the single most dangerous force on the battlefield, and consequently the invention of the Pikeman - a heavily armed soldier, specifically designed to withstand the terrifying cavalry charge.
Military Tactics is one of the two earliest technologies unlocking a Medieval Era unit (the other one is Machinery), and it is slightly easier to beeline than the other (you need Pottery ->Writing->Currency->Mathematics, whereas Machinery requires an extra technology). However, the Pikeman isn't that much stronger than the Swordsman, unless it's facing cavalry of course. If you need desperately a great counter to cavalries you should go for it; otherwise you have little incentive to rush this tech. Huey Teocalli is good wonder, but its bonuses depend heavily on terrain availability, so you will have few good options to use it.
All in all, if you want early progression, go for Machinery instead, which unlocks more interesting stuff overall.
Until the Middle Ages, “tactics” was limited to mostly running at the enemy in a frontal assault, leavened by the occasional maneuver to turn the flank of the enemy line or the decision of when to commit the cavalry to take care of the survivors. Which is not to say that some civilizations were not quite adept at all this: the Akkadians, the Assyrians, the Macedonians, the Romans, the Guptas, and the Han Dynasty. Thus evolved the “Seven Classical Maneuvers” of tactics: penetration of the center, attack from a defensive position, single envelopment, double envelopment, attack in oblique order, feigned retreat, and the indirect approach.
In the late 4th Century AD Publius Flavius Vegetius Renatus wrote De re Militari, described by some historians as "the bible of warfare throughout the Middle Ages." One of the five major sections of this work focused on field tactics, and stressed the role of infantry and archers, because they were cheaper than cavalry and could operate across any terrain. Some 200 versions of the work appeared, translated into every European language. But European tactics were forced to evolve when the Arabs, Mongols and Turks didn't pay much attention to Vegetius’ pronouncements on cavalry.
Tactics underwent another paradigm shift when gunpowder appeared on the battlefield. Black-powder warfare reached its apex in the Napoleonic Wars, which laid down the principles of tactics that would dominate war until the invention of machine-guns, barbed wire, poison gas, tanks and airplanes made them all moot come the First World War. Napoleonic tactics focused on formations and the maneuver of lines, columns and squares, as well as upon the melding of infantry, cavalry and artillery into supporting and integrated branches. It was all rather elegant.
But the First World War and even more the Second changed everything. The Germans developed the blitzkrieg, the British commando operations, the Americans airborne attacks, while the Soviets just bludgeoned their way forward. On the mobile battlefield the old accepted tactics were forced to give way to the feuerkampf (fire fight) between squads and platoons.
And all this doesn't even touch on the history of naval tactics, as triremes gave way to ships-of-the-line to dreadnaughts to battleships ...