In the third aliyah, G-d states that Yom Kippur shall be on the tenth day of the month of Tishrei. This is also the day that Moshe rabenu came down from mount Sinai with the second set of luchos (tablets) and informed the people that they had received atonement for the making of the golden calf. It is a Chassidic principal that we don't celebrate Jewish holidays only to commemorate historical events, but the spiritual revelation that happened to cause the original event happens again, every year on the same Hebrew date. Thus, the prototype Day of Atonement was when G-d forgave the Jewish nation for the making of the golden calf, and the same potential for atonement is repeated every tenth of Tishrei thereafter.
This aliyah states that on Yom Kippur work shouldn't be performed, and that we should afflict our souls. The oral law defines afflicting one's soul as abstaining from eating, washing, anointing, wearing leather shoes, and marital relations.