You need roads to connect a resources (copper, corn , gold etc) to use that resources. Example, you can have you citizans work the farm for 5 or 6 food, but do not get the +1 health unless it is connected via a road or river (you need sailing to use rivers as roads).
A non-resource mine, farm, or cottage does not need a road to be useful except to speed up travel. The one exception is building a railroad on a mine, lumbermill, or quary gives you an extra +1 hammer.