The rabbis considered 'shame' (busha) as one of the three phylogenetic components of the Jewish moral makeup. Together with the practice of benevolence (gemilut chasadim) and compassion (rachmanut). They went as far as to say that whoever does not posses the trait of shame, could be presumed that his ancestors did not stand at Mt. Sinai (an euphemism, to say that he might not be ethnically Jewish).
Besides seeing shame as a natural Jewish trait --in complete contradiction with the alleged Jewish 'chuptza'-- the rabbis explain that 'shame' is a prerequisite for a perfect Teshuba (repentance)
Maimonides writes (1:1) , "When a man or a woman commits a sin... they shall
confess their sin which they have done... by saying, `O Lord, I have sinned,
transgressed and rebelled before You, and have done such- and-such, and I am
ashamed by my actions and will never do it again'.
The rabbis of the Talmud especially praised the feeling of shame during the process of Teshuba.
Why?
Because, unlike guilt, which is a more private feeling, 'shame', consist in the uncomfortable sensation of facing our own flaws in front of others.
The main impediment to follow God's will is that God is invisible. It is extremely challenging to realize His constant presence. Therefore, we are not easily ashamed of doing something wrong in front of Him.
Conversely, if we are capable of feeling embarrassed while confessing our
transgressions to God, it means that we have achieved a very high level of Emuna: the state of awareness of God's presence.
A sincere Teshuba occurs when we mentally position ourselves in front of God, (lifne haShem titharu) and we feel ashamed, as if we were confessing our misdeeds in front of another person.