Can be traded for experience points with Lucius. For each Midnight Shard, you can gain experience; L being the character's level. Players above level 200 will receive the same amount of experience as a level 200. A character can trade up to 40 shards for experience per year. However, an arbitrary amount of shards can be traded for gold.
Note that the formula is not (for N shards). If you level up by using one shard, you will not gain 300 more experience per shard for the next level. Thus, it is slightly better to trade them incrementally, than all at once.