Every time one I hear some fitness teacher say something about engaging one's core I can't help but think I have teleported to a Star Trek episode. And my days of wearing a jumpsuit are long past, thankfully for the rest of the world!
The first time a pilates teacher (who wasn't very good I now know) told me to engage me core, I sucked in my stomach as hard as I could. I was not corrected, which is why I now know she wasn't a very good teacher.
Anatomy lesson here: This is a body's core: