The second eldest child of Claudius and his first with Valeria Messalina, Octavia was probably no stranger to the intrigues of the imperial court even at a young age. When she was ten she saw her mother executed, officially for conspiring against her father. A year later, Claudius married his niece, Agrippina. The new Empress soon broke off Octavia’s childhood betrothal to Lucius Junius Silanus, and persuaded her husband to betroth her to her own son Nero instead. Octavia was married at 13.
Her relationship with her husband and mother-in-law was not good. Nero decided he hated her, and took up first with Claudia Acte** and then with Poppaea Sabina. Agrippina, meanwhile, saw her as a dangerous rival, politically and personally. Octavia’s marriage to Nero had strengthened his claim on the Empire, but it also made her a threat to Agrippina, especially after Claudius died. Her reputation as a virtuous and chaste wife (by contrast with Nero and Agrippina’s antics) and the fact that the popular Britannicus had been her brother, only strengthened her position, especially in the eyes of the Roman people.
It did her little good though. Nero had his mother killed in 59 CE. Three years later, he finally felt secure enough in his power to divorce Octavia on the grounds that she was barren and marry Poppaea. That, however, was not enough for him. Octavia was still beloved of the Roman people and had powerful political supporters. He accused her of adultery and had her banished to an island, then executed. She was only about 22 years old.
*It’s worth noting that most of the evidence we have comes from Nero’s political enemies. A historian more sympathetic to Nero and Agrippina may well have painted a different picture of Octavia.
**She may have been Claudia Octavia’s freedwoman.
Tacitus, Annals 11-14 - Lacus Curtius
Suetonius, "Claudius," Lives of the Caesars - Lacus Curtius
Suetonius, "Nero," Lives of the Casesars - Lacus Curtius
Hurley, Donna, "(Claudia) Octavia, Wife of Nero" - De Imperatoribus Romanis
Claudia Octavia - Wikipedia