The Pasuk in Tehilim says (931:61) ימים יצרו ולא אחד בהם, "When days were created most unique was not one of them." The Midrash interprets this phrase to be referring to Yom Kippur. There are a number of ways to explain this Pasuk in its pertaining to Yom Kippur.
The שפת אמת explains that Hashem created days to serve as finite units of time - ולא אחד בהם except for one of them. This "one" is Yom Kippur because it was not created to serve in this world, but to offer a taste of the world to come. Every Yom Kippur, a very small quantity of עולם הבא penetrates into this world. We see this idea in the Gemara (Yoma 02a) which says that the Satan looses his power to tempt Bnai Yisrael to sin on Yom Kippur. This is because the faces of evil only have influence in this world.
In Vayikra (32:23) it states מערב עד ערב, "from night to night." This may be related to the word תערובת, mixture, alluding to the importance of blending Yom Kippur with the other days of the year. Furthermore, the Pasuk in Tehilim is written as ולא אחד מהם but is read אחד מהם ולו - it is one of them. This also could be alluding to this blending of the radiance of the world to come and of Yom Kippur with the days of the rest of the year. Our challenge is to infuse some of the radiance that penetrates this world on Yom Kippur into the rest of the year.