The quarry provides your town with stone that is needed as payment for upgrades.
The production rate are the number of stones produced per hour. The storage value are how much stone you can store in this quarry. The combined storage of all Quarrys (excluding the Vault capacity) are the total capacity you have and when you reach the total storage limit your quarry stops to produce more stone.
You can have as many stone quarries as you need/want, only limited by resource area available space. The maximum number of stone quarries you can build in your village therefore is 22. Upgrading the stone quarry is necessary to upgrade the barracks and mead hall to the same level.
For a complete tutorial on hyper farming (required after you get to lv 21-22) you can visit the Hyper-Farming page
Requirements : You need a palace of the same level to upgrade a mine to the next level.