They don't, really -- but it just increases the odds that they'd see my work. Historically, the feed has been drunk most of the time.
Plenty of times, people I follow don't even appear in my feed. And vice verse.
Medium is working to make the feed better -- but with the volume of content posted here daily, it still borders on not humanly possible.
I follow around 400 people and several dozen publications. No human way for me to see all the new content published by those I follow in one day.
So following both writer and publication just increases the odds of seeing content we really want to see. :)