Self-disclosure is a process in which one person expresses feelings, goals, wishes, thoughts or whatever they have experienced, felt or thought in their own life to someone or some people that they trust or at least don't care if they know about them. This process creates an atmosphere of openness and trust that allows others feeling in confidence to raise their own voice, to tell their own story, or maybe just make or continue some conversation.
Self-disclosure is crucial for developing intimacy in two or more people, characteristic that is fundamental for growing healthier relationships, because when you are in a relationship (mother, friends, husband, wife, brother, etc.) the basis is trust which is encouraged by openness and trust, specially if it is about their own lives.
So, self-disclosure it is important for communication because fosters an environment of trust and openness and also promotes better relationships based on really knowing each other.