The details of Socrates' last day. Naturally, since he was about to drink hemlock, the subject of the immortality of the soul and of man's fate after death comes up.
Socrates asserts that philosophers, after all, have spent their lives preparing for death--desiring that state in which the soul is separated totally from the body, no longer mislead or distracted by the weakness of the flesh. And those who have practiced philosophy rightly are sure to have a pleasant time of it in the underworld, while those who have given themselves over to bodily vices will find themselves bound to the Earth for a time, which explains why there are ghosts (!).
The soul, Socrates insists, must be immortal. Since things come into being only from their opposites, what goes into death from life must also go into life from death, or else everything would be wholly absorbed by death. Moreover, those forms which are opposite will not admit their opposites in any part, so the soul, which is necessarily Life, cannot have any part of Death.
Something like that, anyway. The arguments are interesting, for the most part, because they are very, very weird. Socrates explains the existence of ghosts, gives a speculative account of the afterlife, investigates the nature of the soul... there's almost nothing in this dialogue that I can agree with, but it is amusing to read, when it's coherent.