The phrase, "Kiss me, I'm Irish," is a reference to the famous Blarney Stone found in Ireland. It is said anyone who kisses the stone is blessed with being eloquent.
The Blarney Stone is a popular tourist destination built into Blarney Castle. It is customary for a person to kiss the stone while hanging upside down. Railings have been built to assist with this. The legend of the Blarney Stone explains that a king saved an old lady from drowning, so she put a magic spell on the stone. The origin of the tradition of kissing the stone is unknown.