What does the shard of blade stone do in Demons soul?

It is the basic component that is needed to add the "Sharp" stat to a weapon. This gives you bonuses based mainly upon you Dexterity, but also Strength.

Many weapons can be upgraded with it:

Broad Sword

Claws

Dagger

Estoc

Falchion

Flamberge

Kilij

Mail Breaker

Parrying Dagger

Pickaxe

Rapier

Scimitar

Secret Dagger

Short Spear

Shotel

Spiked Shield

Spiral Rapier

Uchigatana

War Pick

War Scythe

Winged Spear

For more visit: http://demonssouls.wikidot.com/upgrade-sharp