Stained glass window (Cluny Museum, Paris)
The term Middle Ages refers mainly to the history of Christian and Jewish Europe between the fall of Rome and the Renaissance, around 400-1500 AD. Historians usually divide this into three smaller periods, the Early Middle Ages, the High Middle Ages, and the Late Middle Ages.
The Early Middle Ages begin with the collapse of the Roman Empire , starting about 400 AD. Germanic people invaded the Roman Empire - the Visigoths settled in Spain, the Vandals in North Africa, the Ostrogoths in Italy, and the Franks in France. The Huns formed a European empire and then collapsed. The Angles and Saxons invaded England (this is the time of King Arthur). The Vikings invaded northern France, and raided the Mediterranean. By 600 AD, the Lombards replaced the Ostrogoths in Italy, and the Slavs invaded Eastern Europe.
By 700 AD, new empires were beginning to form. In Spain and North Africa, the Islamic Empire took over. Further north in France and Germany, Charlemagne built the Holy Roman Empire. To the east, in Russia, the Vikings and Slavs got together to build a kingdom. But throughout the Early Medieval Period, in the Eastern Mediterranean the Roman Empire still continued.
The High Middle Ages started about 1000 AD, when the modern countries of Europe began to take form. After the Norman Conquest in 1066, we can see the beginnings of England, France, and Germany. In Spain, the Reconquest begins to push out the Islamic rulers. Italy was still struggling between being part of the Holy Roman Empire and being a lot of independent cities, but kingdoms were forming further east in Poland and Russia. In the Eastern Mediterranean, the Roman Empire (or the Byzantine Empire) lost a lot of ground to the Seljuks at the Battle of Manzikert in 1071, and became much less powerful.
Throughout the High Middle Ages, many men and women of Europe were fighting against the Islamic Empire to take back the Eastern Mediterranean - especially Jerusalem - for Christianity. We call these wars the Crusades. The First Crusade did manage to capture Jerusalem, but after that the Crusades were less and less successful, until finally people stopped trying.
In the Late Middle Ages, the Mongol Empire brought peace to most of Asia, and encouraged trade along the Silk Road. Poland, Russia, and Italy profited from this trade. By the early 1300s, however, Europe suffered from both war and disease. England and France began to fight the Hundred Years' War, which made both England and France much poorer. Germany and Italy fought a long series of wars as well. The wars were made much worse by the Black Death, or bubonic plague, which spread along the Silk Road from China to Europe starting in 1328, killing millions of people and causing the collapse of the Mongol Empire.
By the 1400s, after the plague, Europe looked very different. The wars were over. The end of the Silk Road forced traders to look for other ways to get things from China and India. Explorers began to try to find a way to sail from Europe around Africa to China. In 1453, the Ottomans conquered the last traces of the Roman Empire in Constantinople. In 1492, Spain forced the last Muslim rulers out of Granada (and the Jews). Instead of Europeans depending on the Eastern Roman Empire and West Asia and Central Asia, now they were trying to grow on their own.
The Holy Roman Empire and Charlemagne in World History, by Jeff Sypeck (1997). An exciting and accurate account of the formation of one of Europe's great empires.
Beyond the Myth: The Story of Joan of Arc , by Polly Brooks (1999). Accurate and thoughtful, with good illustrations and maps, though more a biography than a history.
Constantinople: The Forgotten Empire, by Isaac Asimov (1967). This book got many future Byzantinists started on their path. It's out of print, but you can get it used.
A Little History of the World, by E. H. Gombrich (2003). Written in 1935, the history is a little out of date, of course, but it is written to convey the facts of all of human history to young people, and I think it does a good job.