British Citizenship for Irish could be obtained through your birth, or through the birth of any one of your parents or grandparents, in Ireland. This arises because of Britain's relationship with Ireland and its Colonial history.
To determine what form of British Nationality you might have, an analysis of your family's history must be done, and then applying it to the Nationality laws of Ireland that were passed over the years.
For more information on how Irish Nationality could be gained through a parent or a grandparent's birth in Ireland or Northern Ireland, then watch this short video by Philip Gamble:
STATUS OF IRELAND
Up until 31.12.1948, Ireland was within the Crown’s Dominions.
Between 01.01.1919 and 17.04.1949, it fell within the Crown’s Dominions, but not for UK Nationality purposes.
From 18.04.1949 until the present day, it was an independent Republic outside of the Commonwealth, but not considered foreign.
Ireland joined the European Union (EU) in 1973.
Northern Ireland is treated as being part of the United Kingdom. The Republic of Ireland (the southern part of the island) claims Northern Ireland, and has be the source of considerable strife.