You have full control over your information and postings. If you wish to keep certain information private, you'll find privacy settings for various features located in the Edit Privacy link via your personal drop-down menu in the top-right corner of the header.
You have the ability to set privacy settings for your profile, all of your posts, and your custom workouts. Your options include letting "everyone", "only your gym", or "only you" see your information. These settings can be changed at any time.
You will not be able to hide anything from the Gym Admins (ie. your trainers). They will still have access to all of your information. They'll need that access to help you in your fitness journey.
You also have on-the-fly Privacy Settings if you ever want an individual post to deviate from our Profile-Wide privacy settings. For example, if you have all your stuff set to public, but there's a workout you don't feel like broadcasting to everyone, you can toggle the privacy for this specific workout before you Save it.