Obsidian shards are items dropped by the TokHaar monsters within the Fight Cauldron, which is accessible after completion of The Brink of Extinction. The shards are rewarded after leaving the Cauldron, in an amount based on your performance.
With 80 Smithing, players may smelt obsidian shards into obsidian bars at any furnace; 12 shards are needed to produce 1 bar. This grants 50 Smithing experience per bar. The bars may then be used at an anvil to smith obsidian armour, powerful high-level armour that is exceptionally useful against TzHaar and TokHaar monsters.
The shards can also be used to repair any obsidian armour the player has equipped, at a rate of 100 charges per shard.
228 obsidian shards, or 19 bars worth, are needed to produce a full set of obsidian armour, an obsidian shield and all three helmets. (Or 264 shards, equalling 22 bars if, for some reason, you want to make both the platelegs and plateskirt.)