The Avars were a mostly Turkic group of people. We first hear of them living in Central Asia under the rule of the Rouran, in the 400s AD. The Chinese, who lived to their south-east, called the Avars the Juan-Juan. Like other Central Asian people, the Avars were nomadic horse-riders, who herded cattle. When the Gokturks revolted against the Rouran in 552 AD, the Avars took the side of the Rouran, and lost. After they lost to the Gokturks, the Avars fled to the west. They ended up in the grasslands of Russia.
When the Roman Emperor Justinian noticed that the Avars had arrived, he tried to keep them from invading his empire. He paid them in gold to fight his enemies, the Huns and the Slavs, who had been raiding Roman land in the Balkans (modern Eastern Europe). The Avars agreed. They were able to use the Roman gold and their own military skill to conquer a large empire. Soon they ruled most of modern Ukraine and Eastern Europe. But Justinian’s plan failed: the Avars ended up taking over a good bit of the Roman Empire they had been paid to stay out of. Around 568, the Avars also pushed the Lombards out of their home and south into northern Italy. The height of this empire was around 600 AD. In 626 AD, the Avars made an alliance with the Sassanians and attacked Constantinople itself, though Heraclius fought them off. This Avar attack was part of why the Byzantines were too weak to fight off the Umayyads when they attacked a few years later.
The Avar conquests were part of a larger pattern of Turkic people conquering Indo-Europeans and Semites about this time – the Gokturks beating the Rouran, the Seljuks beating the Abbasids, the Ghaznavids beating the Samanids.
By the 700s, though, the Avar kings were fighting among themselves. Their civil war weakened them so much that Charlemagne and the Bulgarians were able to make an alliance and destroy the Avar empire. The end of the Avar empire was around 800 AD. By the 870s people had stopped using the name Avar, and had been absorbed into other cultures. Most of the Turkic invaders were very successful, but in the end the Avars were not.