The government, being the party/or coalition that gains a majority of seats in the HoR, has the authority to make legislation for the people since they voted them in. It can either make specific legislation - the type that got it elected - or make general legislation, being the type that is for the betterment of the people.
Arguements For the Mandate
Section 24 of the Constitution states that the House of Representatives must be "directly chosen by the people", meaning that the government is democratically elected and thus endorsed by the electorate, giving them a basis to claim a mandate;
It is an accepted convention of the Westminster system (upon which Australia's political system is largely based);
The accountability mechanism (with the government being accountable to the electorate) usually ensures that it delivers on the electoral promises it has made and which have been approved by the electorate. If not then the people who elected the government have the ability to vote against them;
Being generally considered to be stronger than the other two types of mandates, it can sometimes be used by the government to pressure the Senate to pass the policies which have been endorsed by the electorate, ensuring they become law; and,
General will of the majority mandates can be used effectively to enable the government to adjust to new and unexpected circumstances that arise during its term in office.
Arguements Against the Mandate
Can be claimed by governments which have not been elected with a democratic majority (i.e. Minority governments, such as the Gillard Government) and are therefore not truly endorsed by the electorate;
General will of the majority mandates can be used to break those promises which have been endorsed by the electorate; and
Australia's majoritarian electoral system in the Lower House (i.e. Preferential voting), with its associated "winner's bonus", amplifies the amount of electoral support the government actually receives, arguably overstating this and undermining their claim to this type of mandate.