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.