To explain this, Yom Kippur is a day in which we are cleansed from sin, it is a day of purity (“For on this day, you will be purified”), where the muck of sin is removed from us; the prophet refers to sin as “dirty clothing” upon us, and the atonement of Yom Kippur is essentially a removal of this “dirty clothing” from upon us, thereby cleansing us from sin and purifying us. That is essentially the “purity” which Yom Kippur brings upon us.
When the impurity of sin is removed from us, the barriers that were created between us and Hashem from the sin are removed, and “the iron wall that separates between Yisrael and their Father in Heaven” is torn; this was said of the destruction of the Beis HaMikdash, where a thick barrier was created between us and Hashem afterwards, and it is also said of all sins in general, which creates a barrier between one and Hashem. Whenever a person feels that he is far away from Hashem, this feeling actually comes as a result of sin, which causes a person to feel distant from Hashem. But Yom Kippur comes and brings purity upon a person, in the sense that it removes these barriers created by sin.
Of the Ten Days of Repentance, it is said, “Seek Hashem, where He is found”, implying that Hashem is closer in proximity to us, during these ten days. But on Yom Kippur, there is an even more special degree of closeness.
The atonement and purity of Yom Kippur removes the sins from upon a person, and now there can be greater closeness between one and Hashem.
When sin is removed from a person, it is like laundering a soiled article of clothing - the more one washes it, the cleaner it will come out; so, too, the deeper teshuvah that a person does, the purer he becomes through the atonement of Yom Kippur, and he will attain a level of “A pure heart You created me with” to that degree. But the less a person did teshuvah, or the less earnest it is, although every level of teshuvah is accepted by Hashem, still, it is not “teshuvah shelaimah” (complete repentance), and it will not bring purity upon a person, unless a person has done true teshuvah.
