Why did Boudicca instigate a revolt against the Romans?

There are at least two ways to answer this question.

First, we can look at the ultimate causes of Boudicca’s rebellion.  The Romans had conquered Britain in 43 BC.  By Boudicca’s time, about 100 years later, not all Britons were completely comfortable with the idea of being ruled by the Romans.  Some British tribes, like the Iceni (of whom Boudicca was queen) valued their independence.  This desire to be independent was surely an important reason why Boudicca rebelled.

However, there is also a more immediate cause of the rebellion.  That was the fact that Boudicca’s husband, Prasutagus died after having been the king of the Iceni.  Prasutagus had been ruling the Iceni as sort of a client ruler for the Romans.  The Romans liked to install client rulers who could help them control a subject population.  They would eventually try to take direct control over the client state.  That is what happened why Prasutagus died.  His will left the kingdom jointly to his daughters and to Rome.  But the Roman officials wanted to keep the kingdom all for themselves and overrode the will.

When they came to enforce this decision, Boudicca was stripped and beaten and her daughters were raped.  Because of these outrages, Boudicca started the rebellion.

Thus, we can say that Boudicca instigated the rebellion partly because of a general desire for independence and partly because of her desire for revenge for the way she and her daughters had been treated.

What sparked Boudicca's rebellion?

Boudicca's husband was Prasutagus, a Celtic tribal leader and client to the Roman Empire. When he died, according to Celtic custom he left half of his lands to Rome and, not having any male heirs, the other half to Boudicca. Unfortunately, Roman law did not recognize the will, because Boudicca was a woman, and so the Romans claimed the entire domain for themselves. Boudicca publicly defied the Romans, which led to her family being severely punished, but her subjects the Iceni and other Celtic leaders rallied to her side. Many of them were angry at having their lands appropriated by Roman leaders. They were also angry at being disarmed by the Romans, a measure taken to ensure the security of the Roman legions busily suppressing Druid leaders in Wales. Essentially, then, the cause of the revolt was dissatisfaction with the client-kingship relationship negotiated after the conquest of the Island by the Romans. 

Boudicca and her followers formed a formidable force. They attacked and destroyed garrisons and civilian populations at Camulodunum (modern Colchester), Londinium (modern London), and slaughtered an entire Roman garrison at Verlanium (modern St. Albans). After a period of very bloody fighting and a number of civilian deaths, Boudicca and her followers were finally trapped and defeated in the Midlands in 62 c.e.. She committed suicide to avoid falling into Roman hands.