The significance of Yom Kippur is that God set aside one day for Israel, when their repentance is readily accepted and their aveiros (sins) can easily be erased.
Kapora actually erases aveiros, which is way beyond what Selicha (forgiveness) and Mechila (pardon) accomplish. Yom Kippur is the one day set aside for this Kapora and the Ramchal points out that they can easily be erased on this day.
This rectifies all the spiritual damage caused by these aveiros, and removes the darkness that strengthened itself as a result of them.
Every time we do an aveira (sin) much spiritual damage is caused and darkness (which includes the concealment of G-d) is strengthened. But the Kapora of Yom Kippur corrects the spiritual damage and removes the resulting darkness resulting from our sins.
Individuals who do teshuva (repent) on this day can therefore return to the levels of holiness and closeness to God from which they were cast as a result of their sins, for it is on this day that a Light shines forth that can complete this entire concept.
To accomplish this erasing of Aveiros we need to do teshuva. Yom Kippur has a special Light (spiritual energy) which enables us to return to the level we were at before we did our Aveiros.
Rabbi Dessler points out that the Teshuva of Yom Kippur is of a different nature and is much more achievable than the Teshuva of any other day. In the Rambam’s Hichos Teshuva, the formulation for Teshuva for Yom Kippur is noticeably different from the formulation for every other day besides Yom Kippur. Perhaps the Ramchal is alluding to this difference when he said above that our aveiros “can easily be erased on this day”.
In order to receive this Light, Israel must keep all the commandments associated with this day.
To access this spiritual cleansing we need to do the mitzvos of the day.
This is particularly true of the fast, since this causes each individual to be greatly divorced from the physical and elevated, to some degree, toward the aspect of the melachim (angels).
The fast is a Torah level mitzvot as opposed to a Rabbinic enactment. By abstaining from our main daily physical activity, eating, our spiritual side is more pronounced and this increase in spiritual character moves us in the direction of the purer spiritual creations, like the melachim (angels).
Other details of this day depend on the particulars of this rectification.
It’s a good day to follow all the mitzvos to the best degree possible.