Note: There are only two natural breaks in the text as Plato wrote it, both of which appear near the end. These notes on the text were made later, sections beginning or breaking off where a new theme or topic is introduced or dropped. I have used sections demarcated according to the Stephanus numbers (the page numbers from the 1578 complete works edited by Henri Estienne ("Stephanus" in Latin)). For Plato, the Stephanus numbers are the standard page references, and most editions of Plato's work contain the Stephanus numbers along the margins.
Socrates opens his case with an appeal to the jury to listen to him openly and to pardon him if he slips into his usual conversational style. His accusers have already spoken against him in the flowery manner common in courts of law, and have warned the jury not to be deceived by Socrates, a skillful speaker. Socrates immediately addresses himself to that issue, claiming that while his accusers' speeches contained great refinement and skill, he lacks the ability to speak so well. However, he remarks, he will speak the truth whereas his opponents uttered only falsehood.
Socrates further contrasts himself with his accusers, suggesting that while their rhetorical flourishes were the result of prepared speech, his speech will be fully improvised, issuing thoughts as they come to him. His accusers' artificial and studied speech would be unbecoming of a man of his age (Socrates was seventy at the time of the trial), and so he hopes to address the jury simply by saying what is true.
He asks the jury's forgiveness if he slips into his usual conversational style. This is his first appearance in a court of law, he explains, and so he is completely unfamiliar with the language of the place. As the jurors might forgive a foreigner for speaking in his accustomed dialect, Socrates asks their patience if he, a stranger to the law courts, might speak as he normally would as well. Rather than pay attention to his style, Socrates asks the jurors to pay attention to the substance of his speech and consider whether what he says is true or not.
The sharp contrast that runs throughout this first section lies between the studied, artificial--and false--speech of Socrates' accusers, and Socrates' own improvised, conversational--and true--speech. At this time in Athens, there were a great many sophists, professional teachers who would instruct the wealthy youth of the city in oratory. Throughout his works, Plato gives a rather unkind picture of these sophists--it seems they were generally considered shallow thinkers who taught budding politicians to overcome sound reasoning with shoddy reasoning by means of flowery rhetoric. We shall see that Socrates has often been mistakenly classed with these sophists, whom he despises. The speech of his accusers, then, comes from careful training with sophists, who have taught them to speak convincingly and yet falsely. By contrasting himself with these men, Socrates at once invokes the common prejudice against sophistry against his accusers and distances himself from their practices. He remarks (17b) that he is only a skillful speaker if by "skillful speaker" is meant someone who speaks the truth.
This first section immediately thrusts upon us the depth and richness of Socratic irony. While Socrates professes to be a plain man who speaks only simple truths, he is employing some very clever rhetoric in doing so. Apparently, it was a common rhetorical practice in the law courts to profess one's lack of skill in public speaking. We shouldn't take Socrates' words at face value: in claiming that he is not a clever speaker, he is in fact showing himself to be very clever indeed. It would be more accurate to say that Socrates is parodying the usual rhetoric (which was undoubtedly employed by his accusers), turning it on itself. He is using rhetorical devices to show the uselessness of rhetorical devices, thereby devaluing his accusers' words. This act of turning his opponents' own words against themselves is typical of the kind of irony Socrates uses so skillfully. We shall see that after this introductory flourish, Socrates does indeed slip into his normal conversational tone, having sufficiently parodied his opponents.
Another point of note comes at 17c, where Socrates claims that his speech will be entirely improvised. The speech we are reading, however, does not come from Socrates' improvised speech but from Plato's well-trained writing. Obviously, this is not a word-for-word transcription of Socrates' speech, but is rather a reconstruction by Plato. We find Plato inserting a further layer of irony here, as the words that we are reading are very clearly not improvised.
The concept of irony in Socrates and Plato can be (and has elsewhere been) discussed extensively. Such a slippery concept is difficult to present concisely. That being said, one (but by no means the only) way to consider the significance of all this irony is to point out the essential flexibility of words and language--how the same words can be manipulated to serve different purposes. The end result might be to persuade the jury (and the reader) to mistrust the rhetorical flourishes of both Socrates and his accusers and to pay attention rather to the justness of their claims. Socrates is firmly convinced that his accusers have slandered him and that careful attention to the facts of the case will make this clear. Thus, in his introductory speech, Socrates hopes to do away with rhetoric and sophistry and to focus the jury's attention instead on the facts.
This is arguably one of Socrates' most famous quotes, and in fact, living the examined life was the main cause of him sippin' on a killer cocktail. But, what does he mean? Why does he think that death is favorable option to living an unexamined life? What does the examined (or conversely, the unexamined) life look like? Another way to think about this is "Why does Socrates so willingly accept his fate?". Just food for thought.