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).
The title may refer to a seat used in Scottish Presbyterian churches to shame people who had committed moral crimes such as adultery or becoming pregnant when unmarried. Since the tune is very jolly it may also be a reference to a parlor game of the same name, where participants write or say something about a player that then tries to guess who made each statement. Or, it may refer to Jenny Geddis throwing a stool at the minister of St Giles Kirk in Edinburgh in 1637, in protest of the new Scottish Episcopal Book of Common Prayer. This is said to have sparked the riot that led to the Wars of the Three Kingdoms. An early version of this melody appears in manuscripts in 1733 and 1734. It is also known as Wrights Rant and Joiners Jig.
This jig probably dates from around 1780, and is one of the most popular and long-lived of traditional 6/8 tunes in history. It is also known by the colorful names Off She Goes for Butter and Cheese and Up She Got and Off She Went. It has been widely published and recorded.