A Piper on the Hob is a house cricket. During the colder nights the presence of a cricket was said to be a sign of good luck. Confusingly, there is another musically unrelated Irish jig of the same name (see the last link below).
This tune was known earlier as New Shields, which may refer to the Tyneside towns of North Shields and South Shields in Northumberland. However, it may also originate from Scotland, where it was popular in the early 18th century.
This tune is named for the Cliffs of Moher, along the Atlantic coast northwest of Lahinch, in County Clare. The cliffs are about 8 kilometers long and reach 200 meters in height.