The house of parliament in which government is formed. At the federal level this is the House of Representatives; in most states it is called the Legislative Assembly (or House of Assembly in SA and Tasmania). Members of the lower house represent specific geographic electorates and are elected by the people of those electorates.
The origin of the term is largely historical. In the United Kingdom the House of Lords and House of Commons originally met in different rooms within Westminster Palace. The Lords chamber was positioned at the "upper" end of the building while the Commons met at the "lower", northern end. So "upper" and "lower" referred to where you were standing in the building.