The Phaedo stands alongside the Republic as the most philosophically dense dialogue of Plato's middle period. It contains the first extended discussion of the Theory of Forms, four arguments for the immortality of the soul, and strong arguments in favor of the philosophical life. It also contains Plato's moving account of Socrates' final hours and his compelling myth about the fate of the soul after death. More than most of Plato's other writings, the Phaedo is in constant dialogue with the Pre-Socratic theories of the world and the soul, in particular those of Pythagorus, Anaxagoras, and Heraclitus.
Philosophically, the Theory of Forms is the most important aspect of the dialogue. Though we find hints toward such a theory in dialogues like the Meno, the Phaedo is the first dialogue where Forms are mentioned explicitly and play a fundamental role in advancing Plato's arguments. Yet Plato does not seem at all compelled to argue for the theory itself. The Forms are introduced without any fanfare by Socrates, and immediately agreed upon by all his interlocutors. Later, in discussing his method of hypothesis, Socrates asserts that he can think of nothing more certain than the existence of Forms, and all his interlocutors agree.
Due to the haste and ease with which the theory is introduced and put to work, a number of clarifying questions are left unanswered. For instance, what is the scope of Forms? Socrates normally alludes to non-material ideas, such as the Form of Beauty, or the Form of Justice, though he also appeals to numbers--such as the Form of Threeness and the Form of Oddness--to relative terms--such as the Form of Tallness and the Form of Equality--and to the Forms of Life and Death. An argument can be made that he also alludes to the Form of Fire and the Form of Snow, which would open the field even wider. We might ask what sort of things Forms are that they can encompass such a wide range.
There are also questions as to what Plato means in saying that the Form of Equality is equal, or in saying that material objects participate in different Forms. More detailed treatments of these questions are given in the Commentary to sections 72e-78b and 100b-102d, respectively.
The Phaedo gives us four different arguments for the immortality of the soul: The Argument from Opposites, the Theory of Recollection, the Argument from Affinity, and the final argument, given as a response to Cebes' objection. Plato does not seem to place equal weight on all four of these arguments. For instance, it is suggested that the Argument from Affinity by no means proves the immortality of the soul, but only shows that it is quite likely. The Theory of Recollection and the final argument seem to be given the greatest import, as both of them follow directly from the Theory of Forms. But while the Theory of Recollection can only show that the soul existed before birth, and not that it will also exist after death, the final argument purports to fully establish the immortality of the soul, and is considered by Plato to be unobjectionable and certain.
The account of Socrates' death gives us a portrait of a man so detached from the needs and cares of his body that his soul can slip away without any fuss at all. Plato does not present this as strict asceticism, though, but rather a lack of excessive concern for earthly things. (In this sense, one could argue Plato's ideal is somewhat similar to the Buddhist "middle way.")