The primary schools have mid-June to the beginning of September off, while secondary schools have all of June, July and August off, though in the last ten years or so the school year has tended to start the last week of August in some schools.
A lot of the Irish system has been in place since the first half of the 20th century when there was a 65-35% split between rural and urban living, and the rural kids would have been expected to help out on the family farm during the busy summer months and the long holidays would allow for this. It has been argued since we are no longer primarily an agricultural economy that this provision should be gotten rid of.