Araby's early history is a number of city-states and nomad tribes being squeezed between Ulthuan's colonies and the then-living Nehekhara's expansions, and being exploited by both. Then within a few years around -2000, three things happened: Nagash was born, the Phoenix King shaved a Dwarven ambassador, and an astoundingly talented young man called Mullah Aklan'd started to build a resistance force to evict the Asur from his home of Fyrus. Before this time, Araby had been largely puppet states of Ulthuan and Nehekhara, and their Gods and their magic were both constructed from the scraps of secrets stolen or gifted from each. By the time Mullah Aklan'd was done, Araby was a unified state with its own religion¹, its own magical tradition based on elemental spirits called Djinn, and a kick-start in technology from secrets wrested from both east and west.
Over the coming centuries Araby managed to evict the Elves from the Arabyan coast and had contributed to the first defeat of Nagash at the hands of the Army of Seven Kings in -1600, but in the aftermath they were conquered by an opportunistic and freshly-arisen Tomb King. For a thousand years Araby's military was used as a cudgel against the remaining Vampire holdouts while in Araby itself, Nagash's first lieutenant wages an endless war against it. It only ends when Arkhan returns to a resurgent Nagash in -150 (which eventually ends in a showdown with Sigmar) and at that point Araby was little more than a fractured land of city-states and nomad tribes once more.
Skip forward a dozen centuries or so and Araby has restored most of its wealth and splendour. In 1240, Arabyan corsairs conquer Sartosa from the Norscans who had been using it as a base to raid Tilea from, and they use it as a base to raid Tilea from², marking the prelude to what the Old World calls the 'Arabyan Wars'. In the 1400s, egged on by Skaven and Daemons, a man named Jaffar reunited most of Araby by force, named himself the new Grand Sultan, and launched an invasion of Tilea and Estalia from Sartosa. At this time Bretonnia is only a few centuries old and the Empire is in the early stages of the Time of Three Emperors, and both look up from their internal conflicts to send forces to defend the southern realms and then to retaliate. In Araby the Crusaders are met by a rebellion against Jaffar's rule and the two forces join sides to wrest Araby from Jaffar's control, one city at a time. After a long and brutal war Jaffar was overthrown and killed, and those from the Old World that didn't want to leave until the last of those loyal to him were stamped out founded the cities of Antoch (Bretonnian) and Sudenburg (Empire) on the southern edge of Araby, which eventually became bustling trade ports.
In modern times, Araby is divided in times of peace and united in times of 'bloody hell, Nehekhara's at it again'. It's wealthy, advanced, and largely focused on internal debates over who gets to call themselves the truest inheritors of Mullah Aklan'd's legacy, not unlike the Empire before Magnus. Sure, Arabyan Corsairs from the Pirate Coast do raid the coasts of the Old World, but so do Sartosan pirates to Araby, so it's just seen as a fact of life instead of a geopolitical hot button. And it's got one advantage that is easy to overlook: it's on the equator. I've said a few times that to an Arabyan perspective, the entire Old World could be labelled Chaos Wastes. Imagine how much better off the Empire would be if Chaos cults were rare, Daemons were mere legends, Beastmen only existed in one isolated pocket, and Everchosen were completely unheard of. Sure, Nehekhara can be a pain, but it's a known quantity and a lot of the time they're open to being paid off.
1. In very early editions when Warhammer was more based on history than fantasy, the religion was the monotheistic worship of The One, fairly obviously based on Islam with Mullah Aklan'd being a Mohammed expy. In later editions it is instead a pantheon based on pre-Islamic Arabian religion with Mulah Aklan'd being more of a Saladin figure.
2. Incidentally, the Norscans had taken it from Settra's forces, who had been using it as a base to raid Tilea from, who had taken it from the Dark Elves, who had been using it as a base to raid Tilea from, who had taken it from Tileans, who had been using it as a base to raid Tilea from, who had taken it from Ulthuan, who had been using it as a base to do colonialism on Tilea from. Sartosa's pretty much always been like that.