Basiliscus was a member of the east Roman aristocracy during a period of bitter struggle between the Roman Empire and a number of ‘barbarian’ groups. One of these groups were the Isaurians, a fierce mountain-dwelling people from south-central Anatolia (which is a big chunk of what is now Turkey) who retained some degree of independence at least until the time of Justinian.
From emperor Leo I's perspective, Isaurian recruits strengthened the imperial army against invasion and provided a much-needed counterbalance to the power of Aspar, the Alan magister militum (master of soldiers).
The rise of the Isaurians within the imperial court ultimately led to one of them, Zeno, marrying Leo I's daughter Ariadne. Zeno had adopted his Greek name so as to be more acceptable to the populace, but it seems the aristocracy, at least, never forgot he was really "Tarasikodissa Rousombladadiotes" (say that 5 times fast).
When Leo I died, Zeno and Ariadne’s son – 7 year old Leo II – succeeded the throne. Eyebrows were definitely raised when ‘barbarian’ Zeno was elevated to co-emperor almost immediately. When Leo II died a few months later, leaving Zeno as sole emperor, the aristocracy struck: Leo I's wife, Verina, together with a court cabal raised her brother, Basiliscus, to the throne. And Zeno skulked off to one of his mountain strongholds.
Basiliscus had led some successful campaigns against the Bulgars, Goths, and Huns earlier in his career, although he had failed miserably in the attemped reconquest of Africa from the Vandals. (Gaiseric managed to destroy half his fleet with fire ships.)
In the end, though, Basiliscus's military experience would be useless. During his year on the throne, he managed to alienate everyone who mattered by allowing a massacre of Isaurians, raising taxes, taking money from the church, favouring the heretical miaphysitism, and even executing his sister Verina's lover.
Basiliscus had only one somewhat loyal force left in the Balkans, and they were kept busy by Theoderic and his Ostrogoths. His Isaurian commander, Illus, who had supported him against Zeno, switched sides — to support Zeno’s return. Zeno bribed Basiliscus's nephew and last remaining supporter and so was able to re-enter Constantinople unopposed. The ‘barbarian’ was back on the throne.
Poor Basiliscus and his family sought sanctuary in a church, and emerged only after Zeno solemnly promised not to execute them. Which he didn't... sort of. Instead he had them confined in a dry cistern until they died. ("But I didn't kill them!" said Zeno.)