The Reaper's War refers to a civil war in the Iron Islands that took place in 500AC.
Lord Durran Harlaw of House Harlaw staged a rebellion against his Greyjoy liege lords in the year 500AC. Tensions between the houses had been high since Damron Greyjoy chose a woman from House Farwynd as his bride, the lady Alannys Greyjoy. The conflict between the houses only worsened during the subsequent second Greyjoy rebellion, when Lord Durran sided with the King's army to help crush the Iron Fleet.
Ultimately, House Greyjoy won the civil war at the Battle of Pyke. Afterwards, Alannys placed Durran's cousin Baron Harlaw in charge of the island and took one of his sons as a ward in addition to neutering their fleet and taxing them punitively.
The Battle of Pyke
The Battle of Pyke was a naval battle between House Greyjoy and House Harlaw where Durran Harlaw led his forces against the castle Pyke. The battle was won when Lord Aeron Greyjoy slew Lord Durran, ending the civil war.