Storage Barn vs Market

The difference is that your laborers will bring resources only to the barn or stockpile closest to the resource, while the vendors employed in the market will actively seek out resources from all around town and try to keep their market stocked with a wide variety of different goods.

When you use only barns, each barn will only contain the resources produced in its vicinity. That means when your town grows (and you do not produce everything decentralized) your villagers will need to walk large distances to obtain a specific resource. But when you cover your town with markets, they will just have to visit the nearest market to obtain whatever resource they need. This will not just save them lots of time they can then spend working, it will also allow villagers to easily consume all of the different kinds of food your village has available, and a greater food variety will improve their health.

By the way: The market will only store resources which can either be consumed by houses or by workshops. There is one important resource which is consumed by neither and thus will not be stored in markets: Stone.