The purpose of coaching is to unlock people's potential to maximize their own performance. It helps them learn rather than teaching or telling them. Let's take learning to walk as an example: most people don't learn to walk by following instructions. One crucial way that coaching helps people is by helping them to see themselves more clearly.
A coach provides the space and structure for reflection that is necessary for learning and growth. They help you understand what your values are and how your actions differ from your established values or goals. Developing leadership is one of the main purposes of coaching because coaching generates open thinking among leaders.