Short answers, pulled from the story.
Gaius Calpurnius Piso was a Roman senator who inherited connections from his father Lucius Calpurnius Piso and wealth from his mother Licinia. He distributed vast fortune among all Roman social classes and was known as an affable orator who sang on the tragic stage.
Emperor Caligula banished Gaius Calpurnius Piso from Rome in AD 40 because he took a fancy to Piso's wife Livia Orestilla and forced her to leave him. The emperor then accused Piso of adultery with his own wife to establish legal grounds for exile which stripped Piso of his standing in the capital city.
Groups of conspirators gathered under Gaius Calpurnius Piso leadership following the Great Fire of Rome which struck the city by AD 65. The plot ended when Milichus exposed the conspiracy leading to arrests on the 19th of April AD 65.
Gaius Calpurnius Piso received an order from Nero to commit suicide instead of facing execution and complied with the command that day. He took his own life on the 19th of April AD 65 while all his properties including the Villa Pisoni at Baiae were confiscated by the state.
The family line suffered repeated destruction across three generations of Roman history as his son Calpurnius Piso Galerianus died in AD 70. Galerianus opposed Emperor Vespasian and was executed for that opposition after surviving the initial purge.