‘Repentance’ is a word that secularists don’t tend to understand well – it sounds strange, and perhaps is primarily associated with guilt. This doesn’t really get at the basic idea of repentance.
The basic idea with repentance is to turn away from sub-optimal behaviour, and turn towards what is good.
Another way to put it is as realizing one is off course (the destination in Christianity being theosis, which is becoming more like the Good, i.e., God), and then to start to work to get back on course.
So, when one ‘repents’ one says ‘I don’t think I’m on course right now, time to get back on course.’
It’s not much more complicated than this. Often, we have emotional signals that we are significantly off course, in certain cases involving guilt or remorse, in others something more like ennui. In other cases it’s just a realization one has probably made a mistake somewhere.
Whatever the case, the point isn’t the emotion – rather, the point is to course correct, to re-orient oneself towards the Good and then get going towards it.