I never really got this.

I've always used it kind of like FireRunner says. I always mentally substitute intensity for body.
I have had some cigars with heavy smoke. You know that thick heavy smoke you feel you can practically chew the flavor out of as it rolls around in your mouth? But it wasn't all that strong in nicotine and didn't have a lot of flavor shifting so without too much surprise the website had them listed as medium bodied, so I'm still lost!