Adonalsium

Who or what Adonalsium is unknown but there is evidence that at one time it was the god of the Cosmere until it (Adonalsium) shattered. Hoid and possibly the original Shardholders were present at the shattering and may have influenced the events leading up to it. Its essence is currently in pieces known as (the?) Shards of Adonalsium. There is evidence that there are 16 shards but no concrete proof.

Shards of Adonalsium

After Adonalsium shattered into its present form the pieces were given to or taken by individuals that then had the powers of the aspect of the Shard of Adonalsium. The shard then shapes the person that held it to further embody the nature of that piece of Adonalsium. After the Shard shaped its holder they could only do that which was part of the aspect of that shard.

The existence of these shards have been hinted at in Sanderson's novels.

“I sense shards of something long ago, a fractured presence, something spanning the void. I have delved and searched, and have only been able to come up with a single name: Adonalsium. Who, or what, it was, I do not yet know.”

—Sazed, preface to Ch. 39 in The Hero of Ages, emphasis added

For example in The Way of Kings on page 275 U.S. Hardback it says "Ati was once a kind and generous man, and you saw what became of him." Ati was the name of the person who held the Ruin-Shard before being killed by Vin holding the Preservation-Shard at the end of The Hero of Ages. Intentionally killing Ati went against the nature of the Preservation-Shard but as Vin had not yet become attuned to it she was able to use its power to her own ends.

Trivia

The name Adonalsium appears to be derived from the Hebrew name for God, Adoni