Short answers, pulled from the story.
Queen Zenobia ruled the Palmyrene Empire, officially as regent for her son Vaballathus, who inherited the throne in 267 at age ten. Zenobia held the actual power, and in 271 she claimed the imperial title for both herself and her son.
At its height the Palmyrene Empire included the Roman provinces of Syria Palaestina, Arabia Petraea, and Egypt, as well as large parts of Asia Minor. Palmyrene forces reached as far as Ancyra in Galatia, which marked the greatest extent of the expansion.
Aurelian defeated Zenobia at the Battle of Immae and again at the Battle of Emesa in 272, then besieged Palmyra. Zenobia fled the city to seek Persian help but was captured by Roman cavalry near the Euphrates and brought back to the emperor.
Aurelian initially spared Palmyra after its surrender in 272 and stationed 600 archers there under a commander named Sandarion. In 273 the city rebelled under Septimius Apsaios and declared a man named Antiochus as Augustus, which prompted Aurelian to march on the city a second time and destroy it.
The Palmyrene Empire emerged from the Crisis of the Third Century, a period of severe Roman instability following the murder of emperor Alexander Severus in 235. The decisive trigger was the capture of the Roman emperor Valerian by the Sassanid king Shapur I at the Battle of Edessa in 260, which left the eastern provinces without effective Roman protection.
Zenobia is an icon of Syrian nationalism. Modern Syrian nationalists viewed the Palmyrene Empire as a distinctly Syrian civilization that tried to free the Levant from Roman rule. A Syrian television series was produced based on her life, and Syria's former minister of defense Mustafa Tlass wrote a biography of her.