Think back to a time before the automobile. What did a coach do? It took a person or goods from point A to point B. Modern coaching does the same thing. It transports a person from one point to another in their personal or professional lives.
To extend the coach as a mode of transport metaphor it's worth reflecting on the fact that the coach had no opinion about the people or goods that it carried. As a vehicle it did not question the route or the speed. The coach carried, to the best of its abilities. A modern life or professional coach has much the same responsibilities: to serve the person being coached, to approach them in an appreciative, non-judgmental mindset, and to value the person being coached as having the resourcefulness that they need to arrive at their destination.
Coaching, in one form or another has existed for thousands of years, and it has evolved over that time. It is difficult to imagine that the athletes of Ancient Greece or the Aztec empire didn't have the guidance of a coach. Initially those athletes were probably mentored by a more experienced sportsman but, as their abilities developed, that relationship must have become more of a peer to peer one, shifting from the instructional, expertise focused basis of mentoring to the developmental features of coaching.
There are many different forms of modern coach: time management, sports, voice, relationship, writing, music, business, to name a few. At the heart of any act of coaching are two, interrelated features: active listening and measured speaking. The coach does not need to be an expert in the field in which they are coaching. Indeed, some commentators would argue that content-based expertise impedes the abilities of a coach. The coach needs to be an expert in coaching itself, able to discern and support opportunities for improvement.
If the person being coached has experienced a high quality coaching dialogue they will probably be able to identify four features that defined that experience. Firstly that the dialogue involved them talking considerably more than the coach. Secondly, that the conversation was principally focused on them, their needs and their options. Thirdly, that their thoughts, feelings or actions have mad positive progress as a result of the coaching conversation. Fourthly, that the benefits of the coaching conversation were achieved in a shorter timeframe than they could have achieved if the coaching hadn't taken place.