How is the government like an agreement between the citizens and the government?

Your question refers to what is commonly known as a "social contract." This concept was outlined by the ancient Greek philosophers, such as Plato, is associated with the idea of natural law (law that derives from nature and applies to all), and was later picked up by European philosophers and social theorists in the seventeenth to nineteenth centuries. Some of the more well-known writers of this time include Thomas Hobbes, Jean-Jacques Rousseau, Immanuel Kant, and John Locke.
Basically, the social contract refers to how humans are rational beings with certain natural freedoms but nonetheless give up some of those freedoms to a political system that they entrust to govern reasonably and fairly. It is important to remember that human rights and freedoms do not come from the government but are protected by the government. So long as the government rules in a fair manner, people are obligated to uphold their end of the contract: act in accordance with the law to maintain a well-ordered society. If people choose to break that contract and subvert the law, then they will be punished according to those rules outlined by the government.
But if the government breaks the social contract and becomes tyrannical, then humans are within their right not to obey the government. This is a common theme in the US with the constant jostling between the state and citizen for control and authority over what seems, at times, to be small issues. Protests and resistance to government control are really fights over the social contract when people feel as though the state has overstepped its bounds. In the US these fights usually end up with a third party—the Supreme Court—to decide which party is in breach of the social contract.