Writing about Mount Nebo (in Arabic: Jabal Nībū) in Jordan, one cannot mention its history, both biblical and more modern.
Mount Nebo in the Old Testament
As for the first mention of the Jordanian mountain, we will find them in the Old Testament, and more specifically in the description of the conquest of Canaan and Exodus after the people of Israel came out of Egyptian captivity. The leader of the Israelites, called Moses, opposed God and therefore could not reach the land of the Fathers. Here are the words that God spoke to Moses:
Climb this mountain of Abarim: Mount Nebo, in the land of Moab, opposite Jericho, and look at the land of Canaan, which I am giving to Israel. You will die there on the mountain you will climb [...] Because you were not faithful to me among the Israelites in the waters of Meriba near Kadesh, in the Cin desert, you did not reveal my holiness among the Israelites, therefore you will only see this land from afar, but you will not enter to this land that I give to Israel.
It follows that Moses, for his sin, could climb Mount Nebo in Jordan and look at the land promised to the Israelites, but he had no right to enter it. A little further, in the same chapter, we can read that Moses actually climbed the hill and died on it, so that Israelis could settle here:
Moses ascended from the steppes of Moab to Mount Nebo, to the peak of Pisga, opposite Jericho. Yahweh showed him all the land of Gilead up to Dan, all Naphtali, the land of Ephraim and Manasseh, all the land of Judah, all the way to the West Sea, Negeb, the district of the valley near Jericho, the city of palms, and unto Soar. [...] There, Moses died in the land of Moab [...], and no one knows his grave to this day. The death of Moses on Mount Nebo.