According to tradition, the idea starts from the desire of St. Francis to revive the birth took place in Bethlehem: in 1223 in Greccio, in Umbria, at midnight he enriched mass with the presence of a living crib. That episode was painted by Giotto in the fresco of Superior Basilic of Assisi. But there are also those who say that the Church didn’t give Francis the permission to celebrate this "unusual" Mass into a church and then the function was taken into a cave.
Now the crib is known all around the world even if its birth is associated to Umbria.