The term Coaching is overloaded.
Coaching is a plain English word, around since ages. It is not surprising that its definition in the professional world remains open. This is evident from its Wikipedia page.
That said, there have been attempts to describe coaching better, acknowledging the wide spectrum it could cover, and yet putting some boundaries to it.
My personal view on the term is still evolving despite having played the Agile Coach role. So far I've kept it simple:
Coaching is not classroom training; it is interpersonal; it creates awareness in individuals and teams; it is more about asking than telling.
Check these links for less fuzzy definitions: