Let's see if I can keep this simple:
The Huns, like the Mongols, originated on the western side of China. Like the Mongols who surged into Russia in the later middle ages and again in the 18th Century, the Huns were a warlike tribe who terrorised the more sedentary folk of Europe in the final years of the Roman Empire. They were related to the other Ugric tribes like the Turks, the Magyars and the Finns, whose languages are similar to one another. The Finns and Magyars migrated onward beyond the Caucasus and Carpathian mountain ranges at around the same time as the Turks pushed on along the Silk Road from China via Samarkhand and gradually took over the Eastern Roman (Byzantine) Empire. Whereas the Huns reached the English Channel by the end of the Roman Empire and turned back eastward, the Magyars didn't reach further west than the Danube until late (around the time of King Stephen). In the 15th Century the Turks first attempted to over-run Austria and reached the westernmost Alps of the Tyrol but could not get past the central massif. The Finns were 'colonised' by the Swedes in the Viking Age. That answer probably 'exceeds the brief' but completes the picture.