Your government is the system of people, laws, and officials that define and control the country that you live in. The U.S. government, for example, is a representative democracy with three branches.
There are many different kinds of government, but they all do essentially the same thing: "govern" or oversee the rules, regulations, and interactions of the people who live under them. For the most part, a government is concerned with public life, though many of the laws that a government like ours establishes and enforces can regulate what happens in private life, too. If you work for the government, you're in public life. If you work for a company, you're in the private sector.