This is in reference to the Desmond Rebellions. These were a series of rebellions in the Irish province of Munster that occurred from 1569 to 1573 and again from 1579 to 1583. It is the second rebellion that your textbook is likely referencing.

The second Desmond rebellion occurred simply because the first Desmond rebellion, while suppressed, was dealt with little beyond that. The Old English (those descended from the Norman invasion of Ireland) resented the expanding influence of the Tudor English in Dublin, who were eager to consolidate control and exert English cultural domination through the banning of Irish customs which by this time were interwoven with Old English law and custom. These Old English also had lands appropriated by the crown for settlement by (new) English colonists, furthering their anger. Beyond this, there was also the fact that most Old English were Catholic and the Reformation in England, and especially the Papal reaction to it, also helped to set the Old English lords against the Tudor crown.

Arthur Grey, leader of the English forces which landed in Ireland during the second rebellion, would eventually be recalled by Elizabeth I in 1582 for perceived excessive brutality, which included the Siege of Smerwick in which a surrendering Papal force was massacred by Grey's orders. Grey's scorched earth warfare would result in both famine in the province and bubonic plague in the city of Cork, where many had fled to avoid the fighting.