"Repentance is the fire which gradually burns up the egotism in us."
When we adopt a repentant attitude we accept that we are aways imperfect and in need of continual perfection. It is this attitude that kills our ego based pride. We recognize our limitations and our lack of perfection and have a feeling of compunction.
Fr. Dimitru Staniloae points out that this egoism is our largest obstacle.
So the greatest and continuous obstacle in the way of our progress to love is egoism. Until egoism completely dies, you can't have true love.... He who loves himself, who is full of self-admiration, who considers himself as the most important of all, can't love others. To love others means to forget yourself, to always go beyond yourself, to consider yourself as nothing. The love of others is consolidated in us by uninterrupted repentance and humility. ...
It is clear that no one can approach or enter this kingdom, this paradise, unless he leaves behind the ocean of numberless sirens of egotism...The attitude of repentance carries with it an awareness of our ego-centeredness coupled with an understanding that this needs to be destroyed for us if we are to be united with God in love and to be able to truly love others. Egoism is the clear enemy which our continual repentance attacks. Repentance is what allows us to make gradual and continual progress against an enemy we all face.
Ref: Orthodox Spirituality, pp 141-144