Amman is an ancient Middle Eastern city, and the capital of the Kingdom of Jordan.
In Biblical times, Amman was the capital of the Ammonites, a Semitic people speaking a language very similar to that of their Moabite and Israelite neighbors and sharing many cultural traits with them - which did not prevent their often going to bloody war. The Ammonites disappeared as a distinct people with the rise of successive empires which dominated the region for many centuries - Assyrians, Babylonians, Persians, Hellenists and Romans - but their memory was preserved in the name of the city which had been their capital. It had many ups and downs in its history, alternately flourishing and shrinking. In the 20th Century Amman became the capital of the Kingdom of Jordan and one of the main cities of the Middle East.
Amman in "Occupation Duty"
Amman was the most western outpost of the Arabs, closest to the territory of the Philistinians. That gave Amman a considerable strategic importance, should Arab support for the rebellious Moabites flare into all-out war with the Philistinians.
The Ammonites are not described as being a distinct people at the time of the story. Presumably they were assimilated - either by the Moabites, as were the Evraioi, or by the Arabs. It is not clear if the Arabs of Amman are politically part of Arabia or a separate principality.
- See e.g.: Atlantis and Other Places, pg. 249, HC.