The exact reason behind a bicameral system of government varies from country to country, however, the second house is generally implemented as a house of review. As such, the second "upper" house is often still representative, but may be representative of a different set of stakeholders.
One example of this is Australia where the upper house, the Senate, is designed to be representative of the rights of the States rather than the people.^(1) Australia is a federation of States which handed overall government on a range of issues (set out in Chapter 5 of the Constitution^(2)) to a central federal government. These powers, before federation, were under the control of the States and as such when they were given up the States wanted to make sure they were not abused or that additional power were not taken from the States.
The Senate is set up to effectively allow the States to have equal representation in the Senate (Section 7 of the Constitution) regardless of differences in population size.
This results in a somewhat effective system of government where the lower house (House of Representatives) is representative of the people themselves and the Senate reflects a separate set of stakeholders.
This system is largely replicated in other Countries where there is a federation, most notably the USA which operates under the same system.^(3)
These systems are set up differently from the UK where the upper house (The House of Lords) was reflective of a different set of stakeholders, being the peerage, than the lower house (House of Commons) which was designed to be truly representative. Whilst the times have changed with the House of Lords no longer been hereditary^(4) the House of Lords still operates as a house of review, designed to be a check on the power of the House of Commons.^(5)