Shards can be used to add new affixes to items or to increase the tier of an existing affix by one. An item can have two prefixes and two suffixes, and each affix can be crafted up to tier 5.

When adding a shard to an item you have a chance to achieve a Critical Success, which upgrades the tier of a random affix on the item in addition to the normal upgrade shard provides. A Critical Success does not cost any crafting materials or Forging Potential, and cannot upgrade an affix above tier 5.
Shards drop from enemies and chests like other items, but can also be created by using a Rune of Shattering or Rune of Removal on an item.
Some shards (and the affixes they represent) only drop in higher level zones, while others are simply less common.

Shards that drop as items are placed in your Inventory when picked up, and can be moved to the Crafting Window (Forge) by pressing the Transfer Materials button. Shards gained from Shattering are automatically stored in the Material Storage.