Table sugar is refined sucrose. Blackstrap molasses is the final by-product of sucrose refining; it is what remains after cane juice has been boiled three times and most of the sucrose has been precipitated out.
What's left contains significant amounts of potassium and minerals, as well as carbohydrates, mainly simple sugars (glucose, fructose) and sucrose. Blackstrap is better than refined table sugar, microbes also require minerals for growth.