This is an example of the chest press with a set of suspension bands. I don't know who the guy is or what type of bands he's using, but there are multiple companies that make the suspension bands. Prices will vary.
It looks like he has it anchored to the ceiling, but you can just as easily put it over a door (that is closing) and do the same exercise.
Muscles being worked: abdominals, trunk stabilizers, pectorals, triceps, and deltoids.