Prussia began as a legacy of the Teutonic Order, a German knightly order that arrived in the Baltic region at the request of a Polish Duke, who wished to convert the hostile Pagans of Prussia as they were harassing and raiding his lands. The Teutons gleefully occupied the area, perhaps too gladly. They established themselves as a state, and became stronger than everyone else in the eastern Europe, fielding a FURIOUSLY disciplined army, and the only perfectly disciplined army in the Medieval age, alongside the Romans (as always) and the Chinese (almost always), as the rest of the world (including the fact that now India had been invaded, and lost old martial traditions) had poor, undisciplined levy armies. They populated the entire area with Germans. Though, by 15th century, Teutonic Order was dealt severe blow in Tannenburg, and started losing, as the superb discipline of the heavily armoured tanks called Teutonic Knights was being countered by the invention of gunpowder, and their once impenetrable fortresses were rendered useless. By 1525, they were wiped out. In that power vaccum, from the ashes of Teutonic Order, rose the German state of Prussia.
It carried the legacy and strong military traditions of Teutonic Knights. At first, Prussia was a small, backwater state in Eastern Europe that didn't have much fame in anything. But they did have the most disciplined army, again. By late 17th century, Prussia had been inherited the Electorate of Brandenburg (in fact, it was inherited back in 1415), making their first forays into Germany proper. At that time, they were a divided kingdom, owning Prussia itself as well as Pommerania and Brandenburg, and divided by the corridor of Danzig of Polish Commonwealth, which had grabbed the land from Teutons of the old.
Though, under the Soldier King and his son, Frederick the Great, Prussia turned from an insignificant backwater state to a grand European superpower, with prestige enough to rival even the huge Spanish Empire, Austria, France and Britain. In the mid-18th century they were in the center of a huge total war in Europe, and Frederick, the genius military man, skillfully defeated all the enemies and captured Silesia. The Austrians and other states of Holy Roman Empire were soundly defeated many times, along with Russians and French armies that managed to get there. By the time of his death, Frederick the Great had left Prussia as a superpower state with a totally unmatched military machine on land, with tactics and innovations that are still used today. Though, his successors chose to stick with his tactics and stop moving with time, and the Prussian army declined as a result. By the time of Napoleonic Wars, they were heavily outdated by the greatest military commander on earth, Emperor Bonaparte, although he had a great respect for Frederick.
With a humiliating defeat at the hands of French Empire, the Prussians made some well-thought reforms, and in a few years they again became the best army in Europe. With defeat of Napoleon in 1812-13, they quickly turned sides and joined almost whole Europe against Napoleon, who had previously reduced them to a puppet state. The army of Prussia was responsible for defeating the great Emperor in Waterloo, he had nearly won before Blucher arrived and chaos ensued.
With Napoleon's defeat, Prussia was one of the most powerful nations in the whole world throughout 19th century. With the rise of nationalism, they were the chief member of German Confederation (precisely the north). In 1866, they defeated the Austrian Empire, once the most powerful empire in the world but now declining, and extended the confederation to entire area of Germany. Fielding the most powerful and disciplined on the earth, they defeated France and took over Alsace-Lorraine, and unified Germany into the Deutsches Kaiserreich, the grand German Empire, in 1871. Prussian military traditions were copied, and the Prussian drill instructors were hired throughout the world. New westernizing nations based their constitutions and systems on Prussia, the last years of Qing Dynasty of the Chinese Empire, and the Empire of Japan following the Meiji Restoration, are the best examples.
They continued to field the best army, and Prussia remained as the leader of German Empire, with Wilhelm I, the king of Prussia, being crowned as the Kaiser, the Emperor of all Germany. Austria remained separate of course. But tensions grew between nations by 1900. In 1914, the Great War started, and again the German Army, built entirely on Prussian traditions, deal the best performance in the war. Alas, in 1918 Germany was beginning to run out of manpower, and a revolution broke out in Berlin. The great Kaiser Wilhelm II was forced to abdicate, and although he had hoped to retain the title of King of Prussia, his hopes crashed. Germany had nearly won the war, but that was the end of Prussia.
Prussia would linger on as a state of Weimar Republic, reduced much in territory. After World War Two and the second great defeat of Germany (again having nearly won the entire war), the area was forcefully taken and given to Poland, and the German population had to move out from there by 1944-45. After that, Prussia stopped to exist.