Why does the parable teach about?
Radak: If you will clean yourself, i.e. repent, even so I will punish you for your sin, for it is so awesome. It says "Kabsi mi'Ra'ah Libech Yerushalayim Lema'an Tivashe'i" (4:14)! Had Yisrael of that generation repented, they would have been saved from the enemy and from exile, but they would have received punishment for their great sin in their land. There are sins that are not atoned for via Teshuvah alone, without afflictions after the Teshuvah 1 . Chachamim (Rosh Hashanah 18a) asked this contradiction, and said that both discuss after the final decree; a decree with a Shevu'ah is not torn - "Lachen Nishbati l'Veis Eli Im Yiskaper Avon Beis Eli b'Zevach u'Minchah Ad Olam" (Shmuel I, 3:4).
Malbim: If you will justify yourself and give excuses, and say that you did not sin, you will be clean in your eyes, but this will make the stain of your sin great in My eyes, for you deny the Mitzvah and the One who commanded about it. One who knows that he sinned, even though he considers himself stained, he is not stained in Hashem's eyes, for his Teshuvah is accepted easily. This is not so if he is clean in his own eyes.
Yuma 86a says so about Aveiros of Kares and Misas Beis Din. (PF)
What is "Neser"?
Rashi: It is a kind of earth. It is rubbed on garments [to clean them].
Radak #1: Some say that it is alum.
Radak #2: some say that it is the earth used to wash the head and to clean everything.
What is "Boris"?
Rashi #1: It is cleansing, like "u'Var Levav" (Tehilim 24:4).
Rashi #2: Some say that it is soap.
Radak: Some say that it is an herb for laundering.
What is the meaning of "Nichtam Avonech"?
Rashi citing Targum Yonasan: [Your sin of the Egel] is like the mark of a stain that is not cleansed. This sin persists forever - "uv'Yom Pakdi u'Fakadti Alehem Chatasam" (Shemos 32:34). All punishments that come on Yisrael, are partially due to the sin of the Egel.