Oh boy. My husband does this, Janna, so I'll tell you what I know about his duties and responsibilities.
Ordering stock. This involves going up and down the aisles with a barcode scanner and logging in the number of items on the shelves. This, I believe, gets plugged into a database, and when the number reaches a certain point, they order more stock.
Scheduling. They have to cover all the hours of operation, and they have to schedule according to employee availability and peak times.
Keeping an eye out for shoplifters, check kiters, etc.
Hiring and firing.
Let's see, what else? Oh yeah. His store has weekly ad flyers that have to be packaged for the postal routes, and that's time consuming. They have to be ordered and set up to begin with.
Merchandising (i.e. those displays you always see? they plan those and have or help the employees set them up. Sometimes, they're set up by distributors, so you have them to deal with, too.)
Community Affairs - with our store (small neighborhood grocery store, btw), they do things like cater for small events, they've donated water and backpacks to the school, and they helped cater/put together a bag lunch for the Parents Night. They also get involved in other things. Don't know how useful this part is to you, though.
Maintenance and general cleanliness of the store. Usually, if there is a big maintenance problem, they'll have to hire someone to fix whatever's wrong.
HTH!