In his famous essay "Civil Disobedience," Henry David Thoreau argues that people are accountable to their consciences first and their governments afterwards. According to Thoreau, the best forms of government perform the least amounts of governing and relegate ethical decision-making to the populace. Although he states that ideally free-thinking and morally-minded people should not need governments, he qualifies this by stating that "I ask for, not at once no government, but at once a better government."

Thoreau's view is that only when citizens obey the dictates of their consciences, even when these are opposed to laws of the land, will governments become better. However, most people blindly serve the government with their bodies or their minds and give no thought to the ethics of what they are doing.

A very few, as heroes, patriots, martyrs, reformers in the great sense, and men, serve the state with their consciences also, and so necessarily resist it for the most part; and they are commonly treated by it as enemies.

The specific grievances against the then-standing government that Thoreau delineates in this essay are the US invasion of Mexico and the legality of slavery. Thoreau fervently opposed both of these issues, and as a result, as he describes later in the essay, he was put in jail for refusing to pay taxes supporting these enterprises. He declares:

Under a government that imprisons any unjustly, the true place for a just man is also a prison.

Now we can come back to the quote in the question. It has to do with what a just man's reaction should be to unjust governmental policies. Thoreau compares the government to a machine and stresses the importance of stopping the machine if it is doing more harm than good. To put the quote in context:

If the injustice is part of the necessary friction of the machine of government, let it go, let it go; perchance it will wear smooth,—certainly the machine will wear out. If the injustice has a spring, or a pulley, or a rope, or a crank, exclusively for itself, then perhaps you may consider whether the remedy will not be worse than the evil; but if it is of such a nature that it requires you to be the agent of injustice to another, then, I say, break the law. Let your life be a counter friction to stop the machine.

Here Thoreau offers various reactions to government injustices. If the injustice is inherent in the running of government, leave it alone to wear itself out. It is also important to weigh the consequences of your actions. However, if in obeying the government you are harming others, then your duty is to disobey unjust laws. This applies counter friction that works against the governmental machine. In your civil disobedience, you stop the metaphorical machine, which is the government, from doing damage to your fellow citizens.

In Civil Disobedience, American transcendentalist Henry David Thoreau implores the reader to “let your life be the counter-friction to stop the machine.” This is primarily a call to action through the idea of individualism.

The idea of the machine refers to the government, which Thoreau contends resembles machinery more than a collection of humans. The machine is based on a system of inequality, and the machine takes advantage of that inequality to maintain and grow power over the individual. The machine feels like too big of an entity to overthrow, so Thoreau is commenting that the only way to change the machine is for all (or a majority of) individuals to civilly disobey. This civil disobedience is not violent or harmful but respectful and morally correct.

When an individual recognizes an inherently wrong aspect of government inequality, such as slavery, that person has a decision. They can either sit idly by and allow the machine to continue, or they can engage in civil disobedience in order to try to change the government policy.

Specifically, Thoreau wrote this essay from prison for refusing to pay a tax which he viewed as inherently unjust. While Thoreau’s action is miniscule when compared to the machine, if a majority of citizens participated, the machine would be forced to change because there would be a nonviolent revolt of sorts.

Thoreau says, in this paragraph,

If the injustice is part of the necessary friction of the machine of government, let it go, let it go: perchance it will wear smooth -- certainly the machine will wear out. If the injustice has a spring, or a pulley, or a rope, or a crank, exclusively for itself, then perhaps you may consider whether the remedy will not be worse than the evil; but if it is of such a nature that it requires you to be the agent of injustice to another, then, I say, break the law. Let your life be a counter-friction to stop the machine. What I have to do is to see, at any rate, that I do not lend myself to the wrong which I condemn.

This means that if injustice is actually a part of government, necessary to its workings, then we must refuse to participate in that government, and it will eventually wear out.  Further, if a government's laws require one to participate in the unjust treatment of others (like under slavery), then one has a duty to break those laws and disobey that government.  If the machine of government runs on the the friction of injustice, then the proper use of one's life is to provide a "counter-friction" in order to halt the workings of "the machine."  The citizen's main goal should be to make sure that he or she does not inadvertently contribute to injustice.  For example, if a government collects tax money in order to support the institution of slavery, an unjust institution, then one must not pay one's taxes in order to live justly.

Throughout "Civil Disobedience," Thoreau uses "the machine" as a running metaphor for government. His essay is, of course, a meditation on the correct course of action to take in a democratic society when one's morals run counter to the actions of government. If a government passes an unjust law, he argues, under some circumstances, the best solution is to break that law. Thoreau is particularly opposed to slavery, and the Mexican War, which he views as fought on behalf of those who sought to expand slavery. This evil, he claims, is the "very Constitution," meaning it is so ingrained in the United States that to simply cast one's vote against it is impossible. So the only thing a person can really do to push back against the "machine" is to break its laws, at least those that a person deems to be unjust, or contrary to higher moral law. Thoreau did so by refusing to pay a poll tax, a decision which landed him in jail, which he described as the "true place for a just man" when the law was unjust. If enough people made the decision that Thoreau made, the state would have to reckon with what amounted to a popular revolt. So in this way, Thoreau, though only a small cog in the machine, hoped to bring about a fundamental change in the way it operated.