The "Stars" (Planets)
Like the circles in Hell or the terraces in Purgatory, the stars in Heaven reflect the nature of their inhabitants. For example, the moon is mottled with moon spots, creating an uneven surface. Likewise, the blessed on the moon are inconstant in their vows. Mars is red and its blessed are all warriors who spilled blood for Christ's cause. The Primum Mobile was the first sphere created and it houses the first sentient beings, the angels.
A lot of the planets don't necessarily have physical characteristics that are reflected in their inhabitants, largely because physicality, space, and environment are not major themes in the book. Instead, much of their meaning comes from their names, which are mostly those of Roman gods. Mercury was the messenger god, known for his speed; thus the souls there were hasty in judging what was truly virtuous and went with the easy answer, fame. Venus was the goddess of love and her inhabitants were too passionate in life. Jupiter was king of the gods and all his inhabitants were just rulers. You get the idea.
The Eagle is a symbol of Divine Justice. Appropriately, it is formed by the souls of just rulers in the sphere of Jupiter. How do we know this? Well, a major clue is that the Eagle talks about Divine Justice, emphasizing how incomprehensible God's justice is to man. Also, at the end of Canto XIX, the Eagle blasts a huge list of corrupt or unjust kings.
The Eagle, as a symbol, has a long history. But the one most relevant for our discussion is the golden eagle of Rome, carried into battle as the Roman Empire's emblem. So how did "Rome" turn into "justice"? Well, remember Justinian? His name should give you a clue. His major contribution to history was codifying and improving all of Roman law. While Rome was known for its conquering heroes, a lot of its conquered peoples found their lives improving after being put under Roman rule. And the 'golden' part of the Eagle is kind of carried over to our Eagle in Canto XVIII when we realize that it is formed by these glowing bundles of lights called souls.
Consider Canto XX, where the Eagle introduces the six souls that make up its eye. You say, why the eye? What does an eye have to do with justice? Well, vision is the one thing in Heaven that can win you more of God's love. Beatrice highlights that Dante needs to perfect his vision. Once one can see things clearly for what they are instead of for what they seem to be, it becomes easier to judge them and assign rewards and punishments to them, (i.e. what the law does). That's why the souls in the Eagle's eye are accompanied by the refrain, "now he has learned." Learning – to Dante – is a process of improving one's vision. Now that these souls have learned what's virtuous, they change their behavior to conform to that idea. This is what gets them into Heaven.
The Three Circles
At the end of Paradiso, when Dante looks upward to see the face of God, he sees three circles instead:
appeared to me; they had three different colors,
but all of them were of the same dimension;
one circle seemed reflected by the second,
as rainbow is by rainbow, and the third
seemed fire breathed equally by those two circles. (Par. XXXIII, 115-120)
Traditionally, these have been interpreted to be the Holy Trinity – the Father, the Son, and the Holy Ghost. Each of these makes up an equal and immutable part of God. This is represented by their "same dimension[s]." The Son (Jesus Christ) proceeds from the Father (God) as we see in "one circle seemed reflected by the second," and the Holy Ghost, according to scholar and translator Mandelbaum, "is the fire of Love breathed by both."
But there's something interesting about the second circle: "within itself and colored like itself, / to me seemed painted with our effigy." "Our effigy" is the image of a man. So the circle of the Son (Christ) has a picture of a man inscribed. This makes sense because Christ was both man and God at the same time. In fact, this is a point of great controversy: how can Christ be all man and all God simultaneously? Quick answer? We don't know. It's called the mystery of the Incarnation and it's this mystery that Dante contemplates at the end of the poem. How can one see the outline of a man in the circle if the man is the same color as the circle? Conventional logic would tell us the man is camouflaged into the circle, but Dante can see him here. In our world, that's simply not possible. But that's the whole point of the "mystery." As human beings, we cannot understand it, but must accept it on pure faith.
Dante, however, gets special treatment, because he's gone on this long hard journey, has purged himself of pride, understands Divine Justice (to the extent which man can understand it), has perfected his vision, and now gets to see God. Because he has begged God to let him remember what he has seen to help him on his poetic mission, God grants him understanding of this last mystery. It comes in a burst of light, but we don't get to see it. Such knowledge is not fit for mere mortals. We say too bad, but that's just the way it works.
Light and Vision Imagery
This one is deceptively simple. All the light imagery represents the Love of God, right? But how it works is a different story. First of all, let's deal with the light of the souls. As King Solomon tells us, "As long as the festivity / of Paradise shall be, so long shall our love / radiate around us such a garment." So this light is also the love that man has for God. The cool thing is that it's not just souls that radiate this light; it's also bodies. But only after Judgment Day. When the blessed souls are reunited with their bodies, their completeness will merit more love from God and they will shine all the brighter.
But how does one increase his brightness? Solomon tells us, "Its brightness takes its measure from our ardor, / our ardor from our vision, which is measured, / by what grace each receives beyond his merit." So it all goes back to vision. Our "ardor" or love for God depends on how good our vision is. There's a saying that goes, "to see God perfectly, is to love Him" and that is exactly what is happening here. Now, the vision thing is interesting because it is reciprocated by God. When our vision is good and we see God for what he is, God sees us seeing him and returns the favor by raining down more grace (unmerited love) on us. This grace is ultimately what makes the souls shine.
For Dante, it's a little different. Since he is mortal, the same rules don't apply. To improve his vision, he needs to build up his visual strength by witnessing gradually more dazzling displays of light. Remember Beatrice getting brighter as she ascends? That helps Dante strengthen his vision. The dazzling vision of Christ and Mary ascending (Christ described as a sun, Mary as a "living star") fortifies Dante's eyes so much that he can bear looking into Beatrice's dazzling smile in the Eighth Heaven.
Finally, Dante's sight receives its final perfection in the "reddish-gold" light, which is the water in the river of the garden in the Empyrean. Beatrice tells him that this beautiful garden he's seeing, with the flowers and bees, is not what's really there. So she urges him to bathe his eyes in the river to perfect his vision. After doing so, Dante sees the "garden" for what it really is: the Celestial Rose. The river lengthens into a round pool, at the top of the Celestial Rose. The buzzing bees turn into golden-winged angels and the flowers with which they stop to mingle are the blessed souls. Thus, the light from God not only clothes blessed souls, but also improves humans' vision so that they can sustain the light of God Himself.