On Shabbat itself the world experiences a renewal of sorts. Like God, we "create" throughout the six weekdays. We complete our work on the sixth day and then celebrate this completion on Shabbat. The next day, we begin anew; Shabbat marks the end of our week-long creation, such that we must begin creating our world once again on Sunday.
Parashat Bereishit tells the stories of two men who committed grave sins: Adam ate from the forbidden tree, and Kayin murdered his brother, Hevel. The Yalkut Shimoni on Sefer Tehillim (92:1) relates a seemingly peculiar encounter between the two. After Kayin achieved forgiveness for his sin, Adam met him and inquired as to what happened as a result of his crime. His son replied that he performed teshuva and earned expiation. Adam immediately lamented, "So great is the power of teshuva - and I didn't know!" The Midrash continues that at that point Adam composed the chapter of Tehillim 92, which praises the day of Shabbat - "Mizmor shir le-yom ha-Shabbat."
Wherein lies the connection between Shabbat and repentance?
The Beit Ha-levi suggested that on Shabbat we express our awareness of the fact that the entire universe operates by God's will. By bringing our creative activity to a halt, we proclaim that the world runs because of God, not because of us. This belief entails the notion that every moment of existence is propelled solely by God. Accordingly, time can be severed; since God renews the world, as it were, at each moment, every second has the potential to exist independently of the past. This concept gives rise to teshuva. Given the Almighty's control over every moment of existence, an individual can request a new beginning, whereby all past deeds are forgotten. Thus, Shabbat and repentance express the same general theme.
Others have explained along similar lines only with a slight difference. Shabbat does, indeed, represent the divisibility of time, only not through our testimony of God's power over every moment of existence. Rather, on Shabbat itself the world experiences a renewal of sorts. Like God, we "create" throughout the six weekdays. We complete our work on the sixth day and then celebrate this completion on Shabbat. The next day, we begin anew; Shabbat marks the end of our week-long creation, such that we must begin creating our world once again on Sunday. (Can this explain the dreariness of Monday mornings [or, in countries where people work on Sundays, of Sunday morning]?) In this manner, Shabbat signifies the division of time into independent units, which, as we explained, forms the basis of the institution of teshuva.