Rune Stones are formed from Runeys, the little colored things that are floating around in the game world. In order to make Rune Stones, you need to harvest 10 Runeys of a particular color (using the Harvester you can get from Candy) and give them to Candy. She'll convert them to a Rune Stone for you. The stones are used in the synthesis of certain items, as well as to open doors (such as dungeon doors). You'll need a Tree Rune Stone to get into the second dungeon.
The library has a bookshelf dedicated to explaining the Runey system, inside the door and to the right.
North Dakota is 10,000 times better than South Dakota. All who disagree are Fascists. Currently playing: Rune Factory: Frontier, ToS2: Ratatosk no Kishi