As a concept, the purpose of government is to work towards the benefit of the given society. As for what constitutes "the benefit of" said society, that's an entirely different story.

The goal of government is to maximize aggregate utility of all people, not just its citizens. That's my normative answer. My positive answer is the goal of government is a compromise between maximizing aggregate utility of its citizens and protecting private property or more generally conserving and institutionalizing privilege. Governments are created for the good of their citizens(voting citizens, not just residents), but over time powerful people and groups will use their power to solidify their privileges in socially harmful ways.

What is the goal of government?

Depends on which government you are speaking of.

Many of them across the globe have different agendas and goals.

Now, if you were to ask, "What SHOULD a good and effective government have as its primary goal?" Well, I would be able to give you a better and more comprehensive answer. But as it stands, with this OP question as you have put forth, I must stick with my second sentence above.

SS

Government is a management tool. It manages resources, services, land, law, public property, protection, and external relations. The means by which it does this and the priorities given to the separate tasks vary greatly from government to government.

And be weary of anyone who tells you it exists for something other than management. All that really reveals is they don't understand the diversity and scope of governments around the world and instead just see what they want done or not done by their own government.