The phrase "simple premise" means a basic or straightforward idea or concept. It refers to something that is easy to understand and doesn't involve complicated or complex elements.
Written in 1967, the book was founded on a very simple premise that every pound of fat on your body can be converted into usable calories. (poundsandinchesdrops.com)
Few movies can mine so much tension from a pretty simple premise, and the acting is strong like you mention. (moviereviewworld.com)