Royal Game of Ur (2600 BC; British Museum)
Backgammon is descended from much older board games from Africa and West Asia like Senet and Tabula and Nard. It's probably most closely related to the Royal Game of Ur, played in Sumer and in Shahr-i Sokhta (in modern Iran) about 3000 BC.
Backgammon in more or less its modern form seems to have been played in Iran by the time of the Sassanid Empire, about 500 AD. About the same time, the Roman Emperor Zeno played a very similar game in Constantinople. By the Middle Ages (about 1050 AD), people were playing backgammon in Europe as well as in West Asia.
All over West Asia and Europe, people used backgammon as a gambling game, betting money on the winner. Because of this gambling, King Louis IX banned backgammon in France for a while, and in the 1500s backgammon was banned in England too. In the Middle Ages, people thought playing this new game of backgammon was a waste of time and would lead you to a bad life, just the way some people think of video games today.