Epsom salt is a very simple chemical consisting of magnesium, sulfate, and some water. The water is tied up in the crystalline structure of the chemical, and we can ignore it.
Magnesium is one of the nutrients plants need to grow. It is however, a minor nutrient which means plants don't need very much of it.
Sulfate consists of sulfur and oxygen. Plants can absorb sulfate directly from the soil and use the sulfur molecule. It too is a minor nutrient for plants.