Geodes are stones that have been made inside accidental holes in rocks. If the rocks have liquids seeping through them, then minerals will be deposited in the holes. It is similar to stalactites and stalagmites being formed inside a cave, but on a tiny scale.

In some geodes the deposits will have grown out from the walls to give bands of mineral. Agate is one of these. In other cases, minerals will grow as crystals. Amethyst is of this kind.

The outside of a geode gives no clue as to what is going on inside, so if you buy a geode in a shop, it is like buying a pig in a poke, and you will not know if you have anything interesting until you break it open with a sharp knock of a hammer.