This verse is a threat delivered to the king by the Babylonians regarding the prophet Daniel. Let's break it down:

"So they came to the king...": The "they" refers to the Babylonian priests and people who were angry and humiliated after Daniel exposed their deception regarding the idol Bel.

"...and said, Deliver us Daniel...": They are demanding that the king hand Daniel over to them. They want him to face their own form of justice, likely punishment, or even death, for destroying their religious system and exposing their lies.

"...or else we will destroy you and your house.": This is the threat. The people are telling the king that if he doesn't give them Daniel, they will revolt and bring ruin upon him and his entire royal family. They're using the threat of violence and rebellion to force the king to comply.

In essence, the verse highlights a power struggle:

Daniel's growing influence: Daniel's intelligence and piety have made him a significant figure, capable of exposing the Babylonian priests' fraudulent practices. This makes him a threat to the established religious order.
The king's precarious position: The king is caught between Daniel, whom he may respect or even admire, and the Babylonian populace, who are demanding Daniel's punishment. The threat suggests that the king's power is not absolute and he relies on the support of the people.
The power of religious belief: The verse demonstrates the intense passion and potential for violence that can be ignited by religious beliefs. The Babylonians are deeply invested in their religion and are willing to resort to extreme measures to protect it.

So, the verse signifies a moment of high tension, with the king facing a difficult decision that could have serious consequences for both Daniel and himself.