The concept of upper and lower houses derives from the Westminster Parliament. One theory is that the lower house was the house of the lower classes and the upper house was the house of the upper classes.
The party or coalition of parties that wins control of the lower house wins control of government, so it could be said that government begins 'down' in the lower house. However, bills passed in the lower house must now go 'up' to the upper house for detailed scrutiny by the members of that house.