When people say "the next thing [we] knew," it means the following thing happened very suddenly.
Let me see if I understand what happened:
1) It was Christmas Eve, and the children wanted to stay awake.
2) They tried to stay awake, but they fell asleep.
3) They woke up and it was Christmas morning.
When you fall asleep, you don't feel it happening. From the children's perspective, they were staying awake, but then they were suddenly waking up on Christmas morning.
Let's make another example:
"I opened the door, and the next thing I knew, the cat ran outside."
It means I opened the door, then, suddenly and unexpectedly, the cat ran outside.
"She was eating lunch, and the next thing she knew, she felt sick."
"They started driving home when the next thing they knew, they had a flat tire."
"He picked up the guitar and the next thing he knew, he had written a song."
The sense of this phrase is that the mind is thinking about one thing, and then it shifts its focus to a different thing very quickly, so there's no thought in between the two events. Sometimes that isn't literally what happens, but the purpose of the phrase is to give the feeling that it happened that quickly. Does that make sense?