At our gym for women, we have several coaches who direct us in our workouts and show proper form for movements. There is a reason, however, that they are called Coaches and not Trainers.
A coach does a lot more than a trainer. A trainer will show you how to do things and will ask you to do the things. Yes, our coaches do that, but there is a lot more involved with being a coach for a person.
make a personal connection
suggest things that will help you reach your goals
get to know you as an athlete, and what your strengths and needs are
become personally invested in your success
encourage you with regard to your whole approach, not just during one workout
talk to you about nutrition
know your physical limitations and help you work around them
act as a resource for you
Having a coach means a lot more than just, "Here's the workout, now go do it." They are a part of the team, as well as the leaders of the team.
What does it mean to "be coachable?"
It is important to remember, our membership includes a coach (more than one!) who will get to know you. Being coachable means listening to the suggestions from the coach, and trying what is recommended. Only by pushing yourself outside of your boundaries will you grow as an athlete, and be able to do more, lift more, and increase your strength and fitness.
This month, try out what the coach is recommending before saying, "I can't do that." Yes, injuries and physical limitations exist; if the issue is trying a new technique, lifting heavier than you thought you could, or lifting far lighter than you want to that day, give it a try and evaluate afterward. You may surprise yourself.
We can all learn a lot from our coaches! Let them teach you their ways and see what happens.