If you are curious about health coaching, but not sure exactly what it is, I understand. There is some ambiguity because like the title nutritionist, anyone can call them self a "health coach". A health coach is someone with a background in health/fitness/nutrition with a specific set of skills to help you make long term lifestyle changes (i.e. behavior change).
The idea is that if you've been eating or thinking a certain way for your whole life, it's not going to be a fast or easy fix, or changed by a few appointments with a personal trainer. We need to get in your head a little more. Although personal trainers are incredibly helpful, they [generally] aren't trained in helping clients change their mindset or nutritional habits.
When looking for a health coach, be sure to look at their credentials. There are certifications available through ACSM, Precision Nutrition, Wellcoaches,and more, as well as various degree programs.