Penitent means deeply sorry, ashamed, and full of remorse. If you feel sorry––or just want to appear to––you should adopt a penitent manner.
Penitent comes from the Latin word paenitere, which means to repent. It can be either noun or adjective. Though it's not restricted to them, penitent often pops up in religious contexts, particularly as a noun, as in, "The penitent threw herself at the bishop's feet and begged forgiveness for her sins."