Applicants with a parent or grandparent born in Ireland or Northern Ireland
If a parent or grandparent was born in Ireland or Northern Ireland, then you have a claim to Irish nationality, irrespective of where you were born.
Northern Ireland is included because it is treated as being part of the Republic of Ireland for Irish nationality purposes.
People born to an Irish parent
If you were born to an Irish citizen (either a mother or father) who was Irish at the time of your birth, then you will have a claim to Irish nationality, irrespective of where you (or they) were born.
If you register as an Irish citizen in this manner, then any children born after such registration will have a claim to Irish nationality. It is therefore possible to pass on Irish nationality to children indefinitely, as long as they are registered before the birth of the next generation.