Leinster is one of the four big parts of Ireland, called provinces. It lies on the east of the Republic of Ireland and takes in twelve counties plus the city of Dublin, the capital. So it is not a city and not a single county: it is the group of counties that includes Dublin. People use the name for the place, and you will also hear it a lot in sport — Leinster is a well-known rugby team. Though actually, when someone says they live in Leinster, they often just mean Dublin or somewhere else in that eastern block, not a special Leinster identity the way a city name would.