For the Shachris Torah Reading we read from Parshas Acherei Mos about the commandments and details of the service in the Beis Hamikdash on Yom Kippur. This includes the throwing of the lots, the casting of the Azazel, and the entering of the Kohen Gadol into the Holy of Holies. For Maftir we read from from Parshas Pinchas about the sacrifices that are particular to this day.
For the Mincha Torah Reading we read the second part of Parshas Acherei Mos, which lists the various forbidden sexual relationships. Discipline is vital for a servant of Hashem. While repentance on Yom Kippur includes all sins, these sins are stressed here as men are subject to strong passions from time to time. This, in turn, causes men to lose their innate holiness and is particularly harmful. The Torah reading helps people to reflect on their own errors and to rectify any mistakes.
The Torah prefaces this list of sins with a paragraph that beings with the words “I am Hashem, your G-d”. The Meshech Chachmah writes that before instructing us with a list of forbidden relationships, G-d tells us that if He forbade these relationships, then we can be sure that we can control our desires because Hashem created us and He knows our limitations. No prohibition is too hard to overcome.
Hashem instructed us on how best to live. It is very unfortunate when men misuse the gift of their bodies. Conversely, one who lives a life guided by morality will have persevered his innate holiness and will be granted blessings from on high.