With citizenship you can apply for an Irish passport, vote in all Irish elections and have access to all government benefits.
A person can acquire Irish citizenship through the following method
Born on the island of Ireland
Anyone born on the island of Ireland before January 1, 2005, is automatically eligible for citizenship. After that date, one or more parents must have Irish citizenship at the time of the child’s birth or have had a legal right to reside in Ireland for three of the four years preceding the child’s birth.
Descent of Irish Family
You can qualify for citizenship by descent if you were born outside Ireland and your parents or grandparents are Irish citizens, once your grandparents were born in Ireland.
Through Legal residence in the State
Persons born outside Ireland who meet the requirements for the length of legal residence in Ireland may apply for citizenship. The application process usually takes 6 to 12 months..
Long Term Residency Stamp 5 and 6
If you do not wish to acquire Irish citizenship but have lived in Ireland for more than 8 years, you may be granted indefinite leave to remain (Stamp 5). Naturalized Irish citizens with dual citizenship who need to travel on a non-Irish passport can apply for a Without Condition Endorsement (Stamp 6) if needed.