Executive career coaches are distinct from job search consultants in that they help people who are employed advance their current careers. They don't simply help with networking and job hunting.
That being said, there are dozens of good reasons to need a career coach, so the specifics of what a career coach will do depend very much on your own situation. They might help with skill building, leadership transition, achieving the next work promotion or setting career goals. You can even use career coaches to decide whether to change fields or explore a new industry.
Working with a career coach will generally begin with a session or two to make sure the fit is good, and to define your goals for working together. Then, you'll get to business. Depending on your needs, your coach may ask you to take aptitude or personality tests. She could even interview coworkers, subordinates and supervisors to get a better sense of how you function in a workplace.
Ultimately, your career coach is a partner in setting and achieving your goals. Often, that begins by understanding your own strengths and weaknesses and what personality traits or unspoken beliefs might be standing in the way of your success.