Regional is bigger than local and smaller than national. The local weather forecast covers your city and perhaps a few suburbs; the regional forecast gives you more: maybe a slew of counties, maybe the whole state, maybe even several states.
People who write dictionaries like to think of regional as being a precise term, having to do with well-defined geographic and cultural areas within larger nations: like regional cuisines, regional customs and even, in places like the Great Lakes, regional weather patterns. But lots of times regional is fuzzier than that. A regional high school has students from more than one town, but just how many towns depends on other factors — the local political structure, the number of kids in the area, and the like.