"What is considered a perfect act of repentance? When one is faced with the same opportunity to repeat the original transgression, but now he does not do it because he has repented... however, when one does not repeat the original transgression, [and refrains from sinning] because now he fears people will find out... his repentance is still accepted, but it is not considered a perfect repentance"
To explain a perfect scenario of Teshuba, Maimonides gives the example of a man who is involved in an adulterous relationship and later on repents. The ultimate test of his repentance would take place if that man is eventually faced with a similar opportunity but now he refrains from repeating the transgression, because he repented, and because he has reached a new understanding: now he realizes that following his material impulses will hurt him, driving him away from God.
However, if that man faces a similar scenario but now he refrains from sinning because he fears somebody will find out about his affair, his Teshuba is still acceptable, but it is not considered a complete Teshuba. Why? Because this man might have changed his conduct not because of his repentance and his renewed understanding, but just because of social embarrassment, fear of losing his job, etc.
A modern example: Very often we read in the news about a public figure, usually someone involved in politics, who was caught doing an immoral act. Many times these people would come in front of the TV cameras and publicly express their regret and apologize for what they have done. This is definitely an act of repentance. However, because of its timing, this act of Teshuba is questionable in terms of its credibility and genuineness. Why? Because the whole process of repentance, regret and apologies happened as a consequence of being caught. It is possible that what prompts this person to repent is his fear to loss his reputation, his job, his family etc., rather than his moral conscience.
Following Maimonides words, the perfect act of repentance in this case would have taken place if, while still involved in an illicit relationship or other immoral act, before being caught and with no external impediment to continue with it, one would decide out of his own conscience, to stop, repent and change.That would be a perfect a and complete Teshuba