There is several reasons for this. First is its location between Asia and Europe meant that migrating groups settled the area, groups such as the Alans, Sarmatians, and Scythians. The Caucasus mountains also have the Georgians, who are believed to have descended from the people of Cholchis in antiquity. Armenians too have been in the region since antiquity. Turkic groups later migrated in the Middle Ages. The Seljuks and later ottomans moved into the southern caucuses. Kurds, Assyrians, and other groups live in the south caucuses as well. The constant migration of people from Asia into Europe as well as from Slavs from Europe have shaped the diversity of the region. The hunnic and later Mongolian empires introduced new groups into the region as well. I'll add edits (on a train) later but that's the gist

Edit: spelling of Colchis