What is the usage of the stones monsters drop? According to the wiki page, adventurers can exchange the gems they collect in the dungeon for money. 


  Magic stones are crystal-like stones that are dropped by monsters. The
  stones can be exchanged at the Guild for valis (Orario currency).
  
  The bigger the stone, the more valis it is worth.


I was wondering, why does the Guild want these crystals? Do they have a use?
According to ja.Wikipedia:

魔石
モンスターの生命力の核にして、冒険者の飯の種。例外なく胸部に存在する。
モンスターを倒して胸の魔石をえぐり出し（アニメでは倒すと肉体が消失して魔石だけが残る）、ギルドで換金するのが冒険者の主な収入源。
魔力が込められており、照明や下水浄化、調理用コンロ、冷蔵庫など、さまざまな道具に用いられる。
胸の魔石を直接攻撃して砕いた場合、モンスターは即死する。



Magic Stones are the core of the monsters' life force, and adventurers' means of living. Without exception, it locates in the monster's chest.
Killing the monsters, gouging the Magic Stones out of their chests (in the anime, the body of the monsters disappear when defeated, leaving their Magic Stones behind), and cashing them in at the guild is the main source of income of the adventurers.
Charged with magic, Magic Stones can be used to create various tools, such as lighting, sewage purification, cooking stove, refrigerator, etc.
Monsters die an instant death if the Magic Stone in their chest is destroyed by a direct attack.

DanMachi Wiki has a bit more details regarding the use of Magic Stones:

Uses

Magic Stone Lamp: A handy and flexible use of the Magic Stone is the production of Magic Stone Lamps. These items give off a dim shine that allows one to see underground or in total darkness. It was once considered as the &quot;century's greatest invention.&quot;
Ignition Device: Magic Stones can be used to produce ignition devices.
Freezer: Magic Stones are used in the production of freezers to preserve food.


Volume 1, Chapter 2 is cited as the source of the information above.