As with many of Plato's arguments, his argument about the nature of the soul is based on analogy with other human activities that can be observed by the human senses.
In this section of the Republic, Plato tries to understand the nature of the soul by comparison with a thristy person. Ordinarily, a thirsty person would drink something, but there are times when a thirsty person chooses not to drink. So too, Plato suggests, the soul has its desires (appetites), but also has times when it chooses (calculates) to check or not give in to its desires. Times exist when the soul desires to pursue something, but the calculating part of the soul advises against this pursuit.
However, Socrates and his interlocutor also determine that just as in the city they find three factions, "the moneymakers, the helpers, the counsellors", (441a; Paul Shorey translation), in the soul they also find a third element, which is the "principle of high spirit" (441a), which can spur on either the calculating or the appetitive part of the soul, depending on the environment in which this "high spirit" was nurtured or raised. An example of this can be seen in children, who tend toward their desires when they are young, but tend toward reason when they are older.