The dialogue is sometimes subtitled, "On the Iliad". Subtitles are usually thought not to go back to Plato himself, being instead a way to help distinguish it from any other dialogues with the same name and give a sense of the subject matter when it is just listed; but it's entirely possible that some of them do -- Aristotle, for instance, refers the Menexenus entirely by its subtitle, suggesting that at least some subtitles were quite early. However, scholars seem to have found the subtitle here to be somewhat odd. The obvious subject of the dialogue is not the Iliad but rhapsody, i.e., public recitation and explanation of the poets. Albert Rijksbaron, however, has suggested that perhaps the Iliad really is in view here, and that it is merely the approach that is indirect. Homer, after all, was not a minor element of Greek culture. But it does perhaps sum up the major difficulty in interpreting the dialogue: it could mean many different things, depending on what exactly one takes the point of it to be.
You can read Ion online at the Perseus Project. It also happens to be one of the Platonic dialogues with a translation by the poet Percy Bysshe Shelley, which you can also read online.
(in order of appearance)
Ion is apparently a professional rhapsode from Ephesus. He is not known outside this dialogue; some have suggested that he is fictional.
The Plot and The Thought
Socrates opens the dialogue by greeting Ion of Ephesus, who has just returned from Epidaurus, where he performed at a festival for Asclepius. One can tell where Socrates will take the dialogue almost immediately from his way of opening discussion:
I must say I have often envied you rhapsodes, Ion, for your art: for besides that it is fitting to your art that your person should be adorned and that you should look as handsome as possible, the necessity of being conversant with a number of good poets, and especially with Homer, the best and divinest poet of all, and of apprehending his thought and not merely learning off his words, is a matter for envy; since a man can never be a good rhapsode without understanding what the poet says. For the rhapsode ought to make himself an interpreter of the poet's thought to his audience; and to do this properly without knowing what the poet means is impossible. So one cannot but envy all this.
Ion agrees, adding that he should know because he interprets Homer better than anyone else. On hearing this, Socrates says he would like an exhibition sometime, but in the meantime asks whether Ion is familiar only with Homer or also with Hesiod and Archilocus. Ion replies that Homer is quite enough, although he can expound others as well when they say the same as Homer. Using the example of the diviner's art, which Homer and Hesiod describe differently, Socrates asks whether a diviner or a seer would expound Homer and Hesiod better when they discussed the topic, and Ion concedes this. Socrates asks whether the diviner would be able to expound them as well when they differ as when they agreed, and when Ion concedes that he would, Socrates points out that then he should, if he knows Homer so well, be able to expound the other poets, because for the most part they talk about the same kinds of things. Ion protests that other poets don't do it as well as Homer, but Socrates argues that if Homer is better, and Ion can interpret Homer, Ion must be able to interpret Homer and the other poets equally well. Ion, rather comically, protests against this on the basis of his own behavior.
The discussion turns to the question of skill or art, with Socrates arguing that if someone has the whole of an art, or the whole skill, the principles governing inquiry and evaluation are consistent (so that, for instance, if you have the whole skill of being able to compare two paintings, you have the skill to compare any two paintings). Ion agrees that this is in general true, but insists that it is wrong here because he interprets Homer better than anyone else, but cannot do so equally well for other poets. Socrates replies that he thinks this means that Ion doesn't have a skill but instead a divine power that moves him like a magnet moves iron. The divine power of the Muses 'magnetizes' the poets, who in turn 'magnetize' rhapsodes like Ion, who 'magnetize' their audience. This is why no poet is able to write every kind of poetry equally well; he does not have the skill of poetry itself, but is instead inspired by the Muses to write dithyrambs, or epics, or whatever. Poetry is a kind of divine madness, and poets themselves are the rhapsodes of the gods themselves. This, of course, makes Ion a second-hand rhapsode.
Ion is obviously somewhat pleased at the description, but somewhat reluctant to accept the conclusion that he is out of his mind when he is engaging in rhapsodic recitation of Homer; he is quite knowledgeable about everything in Homer. Socrates in response argues that different skills involve different kinds of knowledge, so that different passages in Homer would be better expounded by people who have the relevant craft -- fishermen would better expound passages involving fishing, and so forth. Ion agrees with this, but when pressed by Socrates as to which passages he, as rhapsode, interprets best, he insists that the rhapsode interprets all passages. Socrates sarcastically remarks that bad memory doesn't suit a rhapsode very well. Ion sticks to his guns, to comic effect, as Socrates gets him to admit that anyone who is a good rhapsode is a good general, so, since Ion is the best rhapsode in Greece, he is the best general in Greece, at which Socrates expresses bafflement that Ion is going around making a living as a rhapsode rather than a general. Ion answers, apparently seriously, that he doesn't need to be a general because his city is under the protection of Athens, and Athenians and Spartans wouldn't pick him to be general because they think they do well enough on their own.
Socrates is skeptical. calling him Proteus, but wraps up the dialogue by saying that Ion has a choice as to whether he wants to be called a skillful interpreter of Homer or an inspired interpreter of Homer; and Ion chooses to be called an inspired interpreter.
* Rhapsodes were itinerant lectors and storytellers; the Greek word rhapsodos literally means 'one who stitches together stories'. Much of what we know about rhapsodes comes from this dialogue, although there is a fair amount of scattered evidence elsewhere. Rhapsodes would sing a part of the Iliad or Odyssey, but break the performance up with jokes, local stories, and the like; they would also perform other poems, like those of Hesiod, as part of their act. At least late custom, and sometimes law, required them to perform from written texts. The Athenians made rhapsodic recitation a required part of the Panathanaea festival, in which the full set of Homeric poems would be recited by a series of rhapsodes, and this dialogue suggests that this was a relatively common custom, allowing for local variations. It was a contest, and prizes were given out for the best recitations.
* This dialogue is often taken to be quite critical of rhapsodic recitation, but I'm not sure it is. Rather, the criticism is of taking rhapsodic recitation to be a craft or skill. We know from Phaedrus that Socrates doesn't necessarily think that something's being an inspiration rather than a skill is a bad thing, and, whether or not it was written by Plato, the author of Theages takes Socrates' own teaching to be more inspired than skillful (and the magnetized chain of iron links is at least reminiscent of the way Socrates describes living, breathing logos at the end of Phaedrus). What makes Ion a comic character is that he wants to attribute to rhapsodic recitation what would require divine madness and yet also consider it his own skill -- which requires an extraordinarily inflated opinion of himself.
Quotations are from W. R. M. Lamb's translation at the Perseus Project.