According to Torah law, a father has the right to accept kiddushin on behalf of his daughter when she is a minor, and she will be married immediately. A na’ara is in a situation where either she or her father can accept kiddushin on her behalf. Once she passes that stage she is an adult and her father can no longer act on her behalf with regard to marriage.
The Mishna on our daf teaches that in the case of a na’ara, both she and her father have the ability to accept a geṭ for her. Rabbi Yehuda disagrees, arguing that only the father has the ability to do so. All agree that a basic principle is that for a geṭ to work the woman receiving it must understand the significance of the geṭ and recognize the need to guard the document properly.
The Gemara quotes a baraita that applies this rule specifically to a young child who was married. In a related case, Rav Yehuda quotes Rabbi Yossi as saying that a good indication that a child recognizes the importance of an object is if he knows to save a nut that he picks up, even as he throws away a pebble. A higher level of comprehension is a child who knows to return an object that is given to him for a period of time.
These descriptions apply to very young children. Already by age three, a child knows to differentiate between a pebble and a nut, and by four or five he knows to return objects to their owners. While the ability to distinguish between an important piece of paper and an unimportant one may only come at a later age, given the fact that even a small child can be married off by her father, it is important for the Gemara to establish criteria even for children who are this young.