Rhetoric
The art of rhetoric, that is, of speaking well, is the focus of the dialogue. In Greek as well as Roman times, speaking well was considering a skill that could be taught, according to certain rules. We still have this usage in English, when we speak about 'inflammatory rhetoric," that is, a specific use of phrasings, appeals, and kinds of argumentation that are designed to produce a specific effect in the audience. A "rhetorical question" is a question that is not meant to be answered, but rather to heighten the effect of what is being said. ("Are we not men?") Throughout the Gorgias rhetoric is for Socrates a counterpoint to philosophy, because it teaches to flatter, without any consideration for what is good for the audience, and it teaches a kind of expertise without any sense of why it is important, or what ultimate goal it is supposed to achieve. Because rhetoricians are well-paid, and rhetoric was regarded as a useful skill, Socrates' attack on it illuminates by contrast his own conception of philosophy as something beyond use, something valuable in its own right.
Hard Truth
Throughout, Socrates emphasizes that philosophy tells us not what makes us feel good, as does rhetoric, but what is true. Socrates gives very few hard truths throughout the Gorgias, as he largely asks questions, rather than states facts, welcome or unwelcome. But this stance is crucial in helping us understand Socrates's sense of philosophy, as something that necessarily cuts against the world, as something that brings the person who practices it out of harmonious relationship with the world. While the sophist or rhetor easily gets fame and riches, Socrates expects the philosopher—the real thinker as opposed to the charlatan and flatterer—to be misunderstood and his ideas to be rejected.
Humor and Irony
Much has been made of Socrates' "irony," his tendency to pretend that he does not know the answer to his own questions, or his pretended ignorance. (This comes from the Greek term "Eiron," a comic figure in the theater who would play the fool to humiliate boastful people.) The German philosopher Friedrich Nietzsche argued that this revealed a resentful streak in Socrates's thinking—that Socrates was simply a poor, ugly man who passed his time humiliating his social betters. The question of whether Socrates is "playing' this part and being "ironic," deliberately saying things he doesn't mean, is a difficult one to parse, since Socrates' philosophy consists of accepting that he knows nothing and starting from there. Irony might be his way of tricking his interlocutors into the truth, by revealing to them that they know nothing. This playfulness on Socrates' part is contrasted with Polus' laughter, which is disdaining and scornful, and which Socrates rejects as an insufficient form of argument, the same as saying nothing.
Tyranny
The debate about what is good in Socrates' dialogs always leads to the question of government, and the question of government always leads to the problem of tyranny. Tyranny is the system in which might makes right: those who have power are by definition in the right. The Greeks would have had many examples of rulers who simply did the wrong thing, were cruel to others, prospered, and faced no punishment; the figure of the tyrant recurs throughout the Platonic dialogue as the person who couldn't care less about examining his life, knowing the truth, doing the right thing, and prospering anyway, because he is strong. Socrates observes that such a person would be deeply unhappy, and in fact, less free than the people he is tormenting, because he would be slave to his own impulses. Socrates describes goodness, justice and truth as human needs, as a kind of health; a tyrant, Socrates says, is like a person suffering from a tumor. Thus Socrates constantly compares philosophy, the care of the self, to governance, the care for the people, and medicine, care for the body.
Philosophy
Like most of the Socratic dialogues, the specific question at hand quickly opens up into the larger question of philosophy. What is philosophy? Socrates claims that it is the search for the true and the good, which the soul has need of in order not to become sick. In this sense, philosophy is distinguished from other modes of inquiry, which are often situational, like rhetoric—"what can I say that will get the audience on my side?"—because it asks after things that are eternal. The true and the good are true and good eternally. But more than that, philosophy is a lived practice: a daily care for the soul by asking questions, by carrying out thought experiments, and by the regular practice of humility, in knowing that one knows nothing.
Medicine
Throughout, Socrates uses the analogy of medicine to describe philosophy; he compares the philosopher to a doctor of the soul. Medicine gives us two important understandings of philosophy. First, medicine is a body of knowledge, a collection of facts that the doctor has to learn and master, facts that everyone recognizes as unchanging and true. But, more significantly, medicine is also a practice: it is knowledge that it is applied, whose purpose is to know the body and what is good for it so that it can care for it. Philosophy is, similarly, a kind of care for the soul, a way of knowing what is true and good in order to assure the soul's health and well-being.
The Judgment of Naked Souls
The German philosopher Friedrich Nietzsche once observed that Christianity was "Platonism for the people," and the Judgment of Naked Souls has a strikingly Christian flavor to it. What Socrates describes at the end sounds very much like the division on judgment day between the redeemed and the damned. But what this tells us about Socrates's worldview is the sense that the truth can never be arrived at on earth, only in the beyond. The Judgment of Naked Souls also has a strange citational character, because Socrates cites it as a myth, long-dismissed by intelligent people. The task of philosophy consists of guessing how those judges would see us and applying those judgments to ourselves. For Socrates, then, this final judgment is best understood as the kind of self-questioning of the kind that Socrates has been doing throughout Gorgias.