We learned in the Mishna that on Yom Kippur we read Aharei Mot – where we find the commandments to Aharon the kohen gadol about how to enter the Holy of Holies (see 16:1-34). Since the only person who is permitted to enter the kodesh kodashim is the High Priest on Yom Kippur, the choice of this reading seems most appropriate. The Gemara quotes a that adds information about the haftara – Yeshayahu 58, which discusses repentance and the ideal fast day from God’s perspective – as well as the readings for the afternoon service on Yom Kippur. According to the baraita, during Minha we read the laws of forbidden sexual relations (Vayikra chapter 18) and for the haftara we read the entire book of Yona.
The choice to read the laws of forbidden sexual relations on Yom Kippur seems to be an odd one. Rashi suggests that since such sins are relatively common – given that sexual desires are part of human nature – it therefore makes sense to offer a public call to the people to repent from such sins on Yom Kippur. Tosafot says that it is commonplace to find women attending the synagogue dressed in their finery to honor the holy day, so it is necessary to remind the congregation to take care in their interactions between the sexes. Tosafot also mention a midrash that teaches how reading these rules is a hint to God. We are saying to him “just as You commanded us to restrict our activities regarding uncovering nakedness, we beseech You to show sensitivity today and refrain from uncovering our nakedness (i.e. our sins).”
A different approach is taken by one of the later commentaries, Rabbi Yosef Messing in his Gan Naul. According to him, this section of the Torah is read specifically because the Jewish people are careful with regard to these laws, thus publicly announcing them is a statement indicating that we are righteous in our behaviors.