Rawls and Nozick were responsible for reinvigorating rights-based liberalism in the 20th century, saving political philosophy from mere in-fighting among utilitarians, and the superstitions of Marxism. Political philosophy since is largely a response to Rawls and Nozick.
This is a work of genius, though it is frequently misunderstood, perhaps on purpose. Most readers, including important philosophers like Thomas Nagel, simply misunderstand the argumentative structure, with the result that many famous criticisms of the book are irrelevant.
Nozick's thesis is that a minimal state can be justified, but a more than minimal state cannot, except under unusual situations.
Part I of the book is addressed to other libertarians, specifically market anarchists (also called anarcho-capitalists). As such, Nozick assumes libertarian rights of self-ownership (or self-governance). Basically, Nozick wants to show market anarchists that a minimal state can arise without violating anybody's rights, where the rights in question are things that all parties to the debate agree that we have. To do so, he describes a scenario in which security companies come inevitably to have natural monopolies over geographic areas. After providing a highly original analysis of the nature of risk and its moral implications, plus a hugely important discussion of side constraints and moral prohibitions, Nozick establishes that such a monopoly would legitimately prohibit other security firms and independent enforcers from operating in its area, provided it compensates everyone involved. The most natural form of compensation is free security. Nozick then argues that an equilibrium will occur in which the security of all can be provided for with an analogue of coercive taxation.
At the end of this section, Nozick, provided the argument is successful (and there are good reasons to think it is not) has established that an agency provided court, military, and police services in a geographic area will arise without violating rights and without the explicit intention of creating a state.
A very common misreading of Nozick occurs here. Many philosophers think Nozick believes that only a state that does arise in this manner and has this form (of a security company with private shareholders) can be legitimate. Nozick didn't think this and isn't committed to it. Instead, what he believes he has shown is both that a minimal state is desirable (it would arise unintentionally as a result of spontaneous order because it is superior to market anarchy) and legitimate. Nozick can then say that this leaves open whether the state will be democratic and in what way.
The second part of the book is meant to challenge arguments for the more than minimal state. It is also misunderstood, even by very smart people. Nozick does not assume libertarian rights in part II, though he refers to them at times. Instead, his argument consists of three factors. First, he primarily addresses egalitarian liberals (hereafter e-liberals). E-liberals believe that rights to personal freedoms (sexual activity, etc.) are justified, but hold that economic activity can be controlled by government decree. Nozick examines e-liberals reasons for wanting a more-than-minimal state (such as a welfare state or social democracy), and debunks them by drawing analogies between the economic activity the e-liberal would regulate and personal freedoms the e-liberal desires to leave free. If the e-liberal cannot identify a morally salient difference, she is forced to either deny the personal freedom, thus becoming an authoritarian, or admit that the economic activity should remain free, thus conceding Nozick's point.
Another style of argument used in part II is what I will call "the liberal presumption" argument. The liberal presumption is that any human activity ought to remain unregulated by laws unless some strong reason can be shown to regulate the activity. (This can be contrasted against the authoritarian presumption, which Mussolini and Stalin held, namely that any activity ought to be governed unless strong reason can be shown to let it be free.) Nozick addresses e-liberals, who hold the liberal presumption, and then attacks the reasons they offer in support of regulating various activities. He shows that the reasons are based on misunderstandings and bad arguments, thus restoring the liberal presumption.
The last type of argument does not rely on this presumption. Nozick addresses Marxists, for instance, who are not liberals. His arguments against them consists mostly of just showing what's wrong with their position. For instance, Marxist exploitation theory crucially depends upon bad economic theory, such as the labor theory of value, something which was shown false back in the early 1870s. (Almost all contemporary economists would agree with Nozick on this. Marxism is to smart people what creationism is to dumb people, a pseudo-science.)
The result of these arguments is to show that the more than minimal state cannot be justified.
Along the way, in part II, Nozick provides us with some gems. He gives the first major critique of Rawls. The critique is devastating, as Nozick points out mistakes in Rawls reasoning (simple logical errors, etc.) that leave Rawls' project ungrounded. Rawls, for some reason, never responded to this critique. Nozick also analyzes envy, and provides hypothetical histories to arrive at the more than minimal state that uncover its nature (it is logically equivalent to system in which we all own parts of each other). He also sketches a theory of justice in holdings to contrast with Rawls, Dworkin, and others. This theory, the entitlement theory, is very rough, but it provides a welcome alternative to simplistic theories maintaining that all there is to justice is establishing patterns of ownership.
Part III is the least often read and least understood part of the book. Partly, it provides a contractarian argument for libertarianism (see Loren Lomasky's article in David Schmidtz' book, Robert Nozick, contemporary philosophy in focus). It thus contains some of the foundations that Nagel claims Nozick lacks (though this criticism is based on Nagel's mistaken reading.) In part III, Nozick asks us to try to construct a system that allows for experimentation and in which everyone, despite their differences, can find a society that allows them to live out their conceptions of the good. The system that best approaches this is a libertarian framework, inside of which non-libertarian communities may be established provided they respect other, different communities. Part III is sketchy, but contains seeds of brilliant things, and it is too bad it hasn't been explored more.
Overall, I would say that the argument of part I is the weakest, part II is the strongest, and part III the most interesting and ripe with philosophical potential.
If you care about political philosophy, you owe it to yourself to read this book. You also owe it to yourself to understand it. If you find yourself thinking Nozick is making a dumb mistake or begging the question, you've misunderstood. But you'll be in good company.