What does Thoreau mean when he says "Let your life be the counter-friction to stop the machine"?
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.