In 2015 there was an excellent series of radio broadcasts produced by RAI and directed by Adolfo Moriconi devoted to the integral reading of Boccaccio's Decameron by professional Italian actors. In every episode, there was also an introduction and some comments by Professor Alberto Asor Rosa, an expert on history of Italian literature. You can find the podcasts of this radio program on the RAI website.
At minute 26:07 of the first part of episode 9, devoted to the Conclusion of the First Day, you can hear what Asor Rosa explains about the role of the poems present at the end of every Day of the Decameron in relation to the characterisation of the narrators of the novellas and, in particular, what this poem says about the identity of Emilia:
Intanto bisogna dire che quasi tutte queste poesie possono essere lette e interpretate come un riflesso del carattere del personaggio che le dice o le canta. In questo caso, ad esempio, Emilia la lusinghiera canta una canzone, una ballata il cui oggetto è l'esaltazione della sua propria bellezza. Questo evidentemente è un omaggio, una concessione a un tentativo di attribuire a questi personaggi narratori un'identità che altrimenti farebbe fatica ad emergere dal contesto narrativo del Decameron.
It must be said that almost all of these poems can be read and interpreted as a reflection of the personality of the character who says or sings it. In this case, for instance, Emilia the flattering sings a song, a ballade whose object is the exaltation of her own beauty. This is obviously a tribute, a concession to an attempt to attribute to these narrator characters an identity that would otherwise struggle to emerge from the narrative context of the Decameron.
So, this song constitutes a resource of the author to construct a portrait of the personality of Emilia as someone in love with her own beauty.
This is also explained by Dino S. Cervigni in his article "The Decameron's Ballads and Emilia's Happy Song", in Annali d'Italianistica, 2013, Vol. 31, Boccaccio's "Decameron": Rewriting the Christian Middle Ages (2013), pp. 131-171:
First of all, the ten ballads constitute the lyrical,
personal, subjective locus par excellence in which the ten young people express their passions about love — a concept emphasized by Claudio Giunta in his erudite and insightful study on medieval lyric poetry. In fact, Giunta also
points out the artificiality and insincerity of the ballads written before Boccaccio, while emphasizing the Decameron's ballads' lyrical, introspective nature.
Referring specifically to the contents of Emilia's ballad, it's stated:
In summary, Emilia is happy, content and satisfied. In her singing she
appears to be completely alone, immersed in the contemplation of her beauty,
which satisfies her fully. She desires nothing else, for this beauty does not
abandon her; but, rather, it grows more and more as she focuses on it further and
she offers herself to it wholly, even hoping a greater joy in the future.
Therein may very well reside the problematic significance of this initial ballad,
which, according to the Narrator's comments, make several members of the
group think about its meaning. Boccaccio the Narrator situates these lofty ideals
precisely at the beginning of the brigata's experience, on the one hand, to
proclaim what is, at least theoretically and ideally, possible to humans, thereby
enhancing even further the lifestyle based on reason proposed by Pampinea at
the beginning of the day. On the other hand, the first ballad's lofty ideals
provide the Decameron readers with a point of reference to judge the extent to
which all the other lyrical and narrative moments of the masterpiece portray a
reality which falls short of the ballad's initial goals of conduct and aspirations.
If one is willing to accept this reading, one can also understand the reasons
the personage called Emilia has been selected by Boccaccio to fulfill this task.
She has a rather limited prehistory in Boccaccio's works, and consequently she
can be molded to carry out this function in the masterpiece. Because of her
middle position in age, being younger than the three oldest ladies and older than
the three youngest, Emilia may be best suited for this programmatic, yet controversial, role. Furthermore, Emilia, who is chosen to sing the first evening ballad, is also selected to rule over the ninth day, unburdening all from a fixed
topic of storytelling. Most importantly, at the end of her rule, in passing the
crown to Panfilo, she invites him to emendate her own defects and those of everybody else. One can certainly argue that the person who understands virtue, can also understand defects and may wish to amend them.
And yet, even though Boccaccio has Emilia foreground and present to the
entire group those lofty ideals, he does not create a feminine character à la Beatrice or à la Laura. Emilia is a human being who, in her tales, describes human vices and virtues, indeed, more vices than virtues, like all the other
members of the group. In fact, just because of her initial proclamation of lofty
ideals, Emilia's world of tales bears out the tension which is inherent to the
entire enterprise of the brigata's storytelling, and which is created by two opposite tendencies: the lofty ideals of her evening song and the defective reality of her world of tales. Some kind of moral resolution will occur only in her last
tale in Day Ten — a resolution, however, which remedies only in part defective human reality, and never attains the impossible ideals of Emilia's initial song.