From the Super Mario Wiki
The Shamrock Kingdom is named for the many shamrocks that grow throughout the land, much like the Mushrooms that grow in the Mushroom Kingdom. Many Stonehenge-type structures can be found throughout the land. It is also where King O'Koopa had built one of his castles, where he hid the Pot of Gold Coins that he stole from Murphy, a leprechaun resident of the Shamrock Kingdom.
It is possible that Murphy and his Pot of Gold Coins are somehow connected to the Shamrock Kingdom, for when the coins were stolen by King O'Koopa, the bad luck that it brought Murphy triggered a rainstorm which nearly flooded the entire Kingdom.
The Shamrock Kingdom is a very rural place, as the only notable buildings that appeared were King O'Koopa's castle, the Shamrock Inn, and a few other homes. There is a chance that the other residents of the Shamrock Kingdom are also leprechauns like Murphy, but none of them ever appear.