Not mine, all credit to /u/anarchistica
Roman empire split up in two parts in 476. Both considered themselves to be the Roman empire.
Clovis of France converted to Catholicism a century later. Most Germans were Arian Christians. Arians didn't believe in the father, son and holy ghost, and didn't follow the pope. From now on most Germans did.
Charlemagne united France, Germany, north-Italy and smaller countries in between. The Pope made him Emperor.
When he died, his sons got a part each, divided vertically. When the "middle" son died, his part didn't go to the King of France (western part).
Otto of the middle part beat the Magyars (Hungarians) and sort of united the middle and eastern part. He got to be emperor too.
The right to rule "Rome" was called the 'imperium'. They considered this right to have been transferred to Otto. They called this 'translatio imperii'.
Otto's empire was Holy since it was sanctioned by the pope and Roman because his emperor-license was legit. Hence, Holy Roman Empire.
The HRE was important because it was huge, had lots of people and because at some point the Habsburg family managed to stay in power and owned Spain too.
Phasing out of HRE
Protestantism came into being in the 1500s. Luther wanted to reform Catholicism but was criminalized instead. Some areas became Protestant, including the northern Netherlands, northern/western Germany and England.
There was a power struggle between France, England, Spain, the Pope, the Burgundians (later the Netherlands) and the Holy Roman Empire which was dominated by Austria (where the Habsburgs ruled).
Inbreeding had severely weakened the Habsburg line. Charles II lost the northern Netherlands, which were rich and became even richer and very powerful.
This new country, the Republic of the Seven United Netherlands [Dutch Republic], needed all the help they could get. While other were casting out Jews, they accepted them. They also allowed their people greater freedom, although Catholicism was illegal. This relative greater freedom was part of an older tradition. Erasmus, and early critic of the Catholic church, came from Rotterdam.
A French philosopher (René Descartes) and a Portugese Jew (Baruch Spinoza) both living in the Netherlands were at the basis of the "Rationalist" movement in the 16th century.
This was followed up in the 17th century by the Enlightenment. There were new ideas about what gave someone the right to lead a country.
Some people didn't like kings and other rich/religious/noble people being their boss. This lead to the American and French revolutions.
Napoleon managed to grab power in France during the Revolution. He crowned himself emperor and used France's vast manpower to conquer Charlemagne's empire all over again.
Napoleon also beat up the Habsburgs. They had been weakened by the threat of the Ottoman Empire in the south and Prussia, a state in north east of Holy Roman Empire. Now everything was slipping from their hands.
In 1806, Napoleon defeated the last emperor and dissolved the empire.
After the HRE
Napoleon was defeated in 1813. In an attempt to keep France in check, the Dutch Republic, Belgium and Luxembourg were turned into one country. Unfortunately, the English decided to make it a kingdom: The United Kingdom of Netherlands.
The Dutch Republic had been dominated by Stadholders, people who held the place (stad) of the king. Fortunately for us, the first three were very competent. The first one, William of Orange, was followed by II and III. The third one is known in England as King William of Orange, because he conquered it. He fell off a horse and his line died with him.
The first king of the UK-NL, William I, was the descendant of the brother of William of Orange III. He was a moron who forced the power of the Dutch Republic on the Belgians. They had far less power and were looked down upon because they were Catholics. Despite being in the majority they had less seats in the government.
Prince William II was better liked in the south and offered to become their king (instead of his dad!). It didn't happen and in 1830 came the Belgian revolution. They lost to William II but France showed up and threatened war.
France's army was of course much more powerful than William II's army. Russia couldn't help because they had rebels. Prussia couldn't help because they had to secure their border with Russia. No one else wanted to help.
Funnily enough, Prussia benefited most from this. Now they had no competition in the Holy Roman Empire, even though that was King William I's intention. They gobbled up all the smaller states but let Austria be.
In a supreme show of karmic rebalance, Bismarck tricked France into declaring war on Prussia in 1870. There were treaties in place since the HRE that obliged German states to help each other if attacked (not if attacking).
France was swiftly beaten. A year later, on 18 January 1871, Wilhelm I was crowned emperor or Kaiser (after Julius Caesar). Once again, the 'imperium' had 'translatio-ed'.
Eastern Roman Empire
Remember how the Roman Empire split up in two parts in 476? In 1453 the Ottoman Empire destroyed the last remnants. However, to the north there was a growing power whose rulers thought of themselves as the rightful successors of the Emperor of Byzantium.
This power, Muscovy, eventually turned into a huge country called Russia. The emperor of Russia was called a Czar, from Caesar.