Cebes brings up Socrates' Theory of Recollection, which claims that all learning is recollection. Simmias cannot quite remember the proof of that theory, and asks for an explanation. Socrates begins by pointing out that we can be reminded of one thing by being made conscious of another thing. For instance, if one sees a lyre or an article of clothing that belongs to a beloved, one will immediately be reminded of the person whose lyre or clothing it is.
Socrates now re-introduces the Theory of Forms, making Simmias agree that there is such a thing as Equality itself--something that is independent of any particular case of equality such as equal sticks or equal stones. We know this Form of Equality, because it comes into our minds every time we see instances of equal objects. However, Socrates points out, equal stones or equal sticks may look equal from one point of view and unequal from another. Nonetheless, we would never be tempted to suggest that Equality itself is unequal. Therefore, the sticks or stones that are equal cannot be the same thing as Equality, since they can sometimes be unequal, and Equality itself never can be. If the equal things are different from Equality and yet can bring Equality into our minds, they must somehow remind us of the Form of Equality. We are aware that the sticks or stones fall short of being perfectly equal, but to be aware that they fall short, we must already have an idea of what it means to be perfectly equal; that is, we must already know the Form of Equality.
We become aware of the equal sticks and stones through our senses, and similarly sense their deficiency with respect to true Equality. There are no instances of perfect equality in the sensible world, and yet we have had this notion of Equality for as long as we have been alive. Socrates infers that we cannot have come to learn of Equality through our senses, but that we obtained our knowledge of it before our birth. And if this holds true of Equality, it should hold true of all the other Forms as well. It would seem that we lose knowledge of these Forms at birth, and it is through a process of learning that we come to recollect them and know them again. This is why Socrates claims that all learning is recollection.
Next, Socrates presents an alternative explanation of the same thing. Someone who truly knows a subject ought to be able to explain it to others, yet most people cannot explain the things that Socrates has been explaining to Simmias. If they cannot explain these things, but can be brought to recollect them to such a point that they might be able to explain them, they must have acquired knowledge of them in some past life that they forgot at the moment of birth.
Simmias and Cebes agree that Socrates has shown that the soul existed before birth, but they remain unconvinced that the soul coheres after death. Socrates remarks that this has already been proved, if we combine the Theory of Recollection with the Argument from Opposites. The Theory of Recollection shows that the soul existed before birth, and the Argument from Opposites shows that it must have been born from out of death. Bearing in mind that the soul has to be re-born after it dies, Simmias and Cebes are forced to acknowledge that it must continue to exist after death.
The Theory of Recollection is laid out in more detail in Plato's Meno, and the discussion in the Phaedo alludes to, and seems to assume prior knowledge of, this earlier discussion. The Phaedo and the Meno are consistent, though, and the presentation of the theory in each dialogue can stand on its own.