I was surfing over to the main Fitcast site (instead of going directly to the podcasts) when I saw this great video.
They refer to them as the "Band-Resisted Anti-Rotation Press." I've been doing these for a couple months, just calling them "Band Pallof Presses." The Pallof press is a press done against sideways-pulling resistance, generally cable resistance, in order to strength your torso's ability to resist unwanted rotation. In other words, to keep you lined up straight and tall even when weight, opponents, or accident attempts to pull you out of that form. I'd been doing Pallof presses at my gym before work, but occasionally I'd want to set up the cable station for my clients and not have to swap out handles for my workout . . . so I started using some handy tubes and bands instead.
Like the Pallof press, you don't really need to load these very heavy. Concentrate on form and when you can complete all of your goal reps with ease, you move up a little bit. A small bit of resistance goes a long way - you want to ensure you're in proper posture and using good form, otherwise you're defeating the purpose of the exercise.
Good stuff, and I'm sorry it took me 8 months to find the video.
1 hour ago