Long ago there was a plot to destroy Adonalsium. It failed. However, it is known that some unknown time later, due to unrevealed events, Adonalsium was killed and shattered by the sixteen eventual Shardholders (and others in attendance), per WoB, the letter, the second letter, and from what Khriss said in Secret History. Thus, Adonalsium was intentionally shattered into sixteen pieces, known as Shards of Adonalsium or 'Shards' for short - which are pieces of the power of creation itself - and that they were then picked up by those sixteen now Shardholders. So, those who killed Adonalsium were a combined force. What they were trying to get was evil. Hoid, apparently, was present at the event. Frost is also well aware of the event:
|“|| "Anyway, there was a God. Adonalsium. I don’t know if it was a force or a being, though I suspect the latter. Sixteen people, together, killed Adonalsium, ripping it apart and dividing its essence between them, becoming the first who Ascended."
" ... Some wished for the power; others saw killing Adonalsium as the only good option left to them. Together they murdered a deity, and became divine themselves."
"So ... my world, and everyone I know, is the creation of a pair of ... half gods?"
"More like fractional gods. And ones with no particular qualifications for deityhood, other than being conniving enough to murder the guy who had the job before." 
Also, it is not random which of the sixteen Holders got which Shard. And, Shards very rarely change hands.
Brandon often refers to Adonalsium as male in Q&As. He has not yet revealed why, when shattered, Adonalsium split into both male and female Shards.
Adonai is the Hebrew name for Lord.
While the sixteen people referenced above (and perhaps some others) were instrumental in the Shattering, it may have been Adonalsium’s own plan they were carrying out, whether they knew it or not.
However, if that theory is correct, it’s possible that Hoid is on the wrong end of things with whatever he’s trying to do, and that Frost is justified in admonishing Hoid (in the second letter) that they are like children stumbling around in the workshop, and may well do more harm than good. Then again, it’s just as likely that whatever Hoid is trying to do is exactly what Adonalsium expected and intended to be done.
Also possible is, a little theory still not proved by thereal.shadow, that Hoid himself, the man with the many names, is the remaining part of Adonalsium, just like the remaining part of the Stormfather is a very powerful spren. Not like the other Shards, he isn't another person, he is the immortal part left from Adonalsium. That would also explain many things:
- The way and plans Hoid follows (he maybe just tries to let the gigantic plan from Adonalsium work out).
- On the question of Dalinar, Hoid responded that he's not a Shardholder. Also, he said that he had his own plans and stood on no one's side, and he would watch the world burn, with tears in his eyes, to get what he is there for. This means that first of all, he HAS the power to do so, while he isn't one of the direct gods of this world, which also means that he is powerful enough to avoid the others. Also, who else would gain anything from destroying another world, except somebody who could as easily create a new one?
Q&A with BrandonEdit
Q: Are you ever going to do a big story about Adonalsium and take it out of the shadows?
Q: Before Adonalsium shattered, was it consciously opposed by something, be it people or another cosmic force? Is whatever opposed it still around?
A: Yes. Yes.
Q: Was Adonalsium shattered intentionally, and if so, was the intention malevolent?
A: Yes, and RAFO.
Q: If Adonalsium shattered with intent, will he always shatter to the same Shards?
A: It is plausible that he could be shattered in a different way.
Q: So it could've been different Shards?
A: Yes, that's plausible.