Your profile
Fix your name and email, see dependents, and review what you are attending.
Profile is you: name, email, and a summary of dependents and attendance.
Edit
Edit to change your name or email. Use an email you actually read — password resets and family approval go there.
Booking preference
Some gyms let you choose whether you book for yourself, or only for people you manage. That control is on the profile when the gym allows it.
Password
Change your password from the account/auth screens (forgot password if you cannot sign in). Profile itself is details, not the password form.