There are sins that can be atoned for immediately and other sins which can only be atoned for over the course of time.
Moses Maimonides, Laws of Repentance 1:4
There are many levels of repentance through which one draws near to the Holy Blessed One. And although there is forgiveness in relation to each kind of repentance, the soul does not become completely purified...unless one purifies one's heart and properly conditions one's spirit.
Rabi Jonah of Gerona (1200-1263) Gates of Repentance, The First Gate
I decided that I wanted to become a Jew when I was 15, but did not act upon that decision until I was 30,twenty seven years ago. Shortly after I turned 30 I began studying with Rabbi Leffler of the Reform Congregation in Lexington, Kentucky. Those weekly conversations we had made an indelible mark on my life and my soul. In one of those conversations Rabbi Leffler drew a diagram on the chalk board that sat in his office, like the one to the right. He said that some religions place their emphasis on the leg of the triangle between "me" and "G-d" with the idea that if one "gets right with" G-d through faith and prayer, that relationships with others will fall into place. But, Rabbi Leffler said, Judaism places its emphasis on the base of the triangle, the connection between "me" and "others," and that by working on our relationships to others, through following the mitzvot, that through building those relationships we will build our relationship with G-d.
So what does that have to do with the passages from the medieval Jewish thinkers (above) about repentance and atonement (t'shuva)? The vast majority of sins for which Jews must repent and atone are sins against others. I have mentioned previously the beautiful Ashamnu ("We have trespassed") prayer of Yom Kippur. Here are some of the sins listed: "we have dealt treacherously; we have robbed; we have spoken slander; we have acted perversely...we have done violence; we have practiced deceit; we have counseled evil; we have spoken falsehood...we have oppressed...we have dealt corruptly...we have led others astray." These, the majority of the sins in the prayer deal with acts against our fellow humans, not acts against G-d.
For the sins we have committed against G-d (such as blasphemy), our regret, rejection and resolution to sin no more can bring immediate repentance and forgiveness. But our sins against others often require us to perform acts of atonement, of restitution and restoration; not unlike in 12 step programs (Alcoholics Anonymous for example) where in order to change the individual must make amends to those they have wronged (unless to do so would bring further harm). Repentance and forgiveness can only come over time, as we work on our relationships with others.