The 12th July is the day on which the traditional Orange parades are held in Northern Ireland. On the Saturday before the 12th there is an Orange parade held in Rossnowlagh, in County Donegal. It is the only such parade held in the Republic of Ireland. I was at yesterdays parade. There were lots of marchers there from Northern Ireland. Also marching were representatives of some Orange lodges in the South, including this group from Leitrim.
If you want to get background information on the history of Orange Order (and I recommend that you do) just look it up in Wikipedia.