My opinion:
The reason why we need resource is that it is the only material to make/construct something. For example, I need a ship. It costs mostly Lumber, Metal and some Precious stone (to make a compass, binoculars). Although we can buy all material or even a whole ship from the market or from the traders, it takes lots of Electrum

. Exploiting resource is a cheap and effective solution
Improvements are built by the government (under the King's order), guarded by players using it and/or the army because it doesn't take just a couple of tree logs to build a Wind Mill or a Mine

.
Players get more resource by exploiting it from the improved-hex, however, each improvement has a capacity of worker in it. Either the government or the players themselves get involved in Expanding the improvement. Each player must spend several APs for one working shift in oder to receive resource in an improvement.
After a siege or an assault, the improvement will get damaged no matter what the result of the battle and must be repaired before in use again. It costs resource taken from neighbor areas and several turns to repair the improvement. This mostly is done by the government (and the players' donation). The winner of the battle controls the improvement that the hex has.
Some improvements/kind of resource and its usage I can summarize:
Hex | Resource | Usage | Improvement |
Plains | Cereals | Trading, alchemy | Wind Mill |
Mountains/Hills | Metal, precious stone, stone | Trading, build/construct/repair stuff | Mine |
Lava/Volcano | Sulfur, gas | Trading, improve siege weapon damage | Forge |
River | Gold, precious metal | Trading, making stuff, used instead of electrum | Water Mill |
Dead land | Souls | Enhance spells of its owner (can't trade) | Graveyard |
Forest | Lumber, rare plants | Trading, build/construct/repair stuff; alchemy | Tree houses  |