Epsom salts have magnesium in them. Magnesium is absorbed a little thru the skin, and it improves circulation where the person soaks. Small blood vessels close up during inflammation and nutrients in the blood then cannot get to where they are needed.

Magnesium also works orally, but in parts of the body that are not receiving good blood supply it doesn't reach where it is needed.

Magnesium helps with pain because it blocks calcium which activates the NMDA receptors in nerves that signal pain response. So magnesium is calming and reduces discomfort.

Epsom salts are especially good for people with Raynaud's syndrome, where the hands and feet get really cold. My son uses soaks for his hands when they bother him.

If you soak in a bathtub for a while (up to an hour) that has epsom salts, your muscles will be more relaxed, your skin softer and you will in general feel much better.