In the Bible, what does "The power of the dog" refer to?

The word dog in the Scriptures often means a wicked person. When he says, "Deliver my darling from the power of the dog," it is a prayer that God would deliver His only Son from the hands of wicked men.

https://biblehub.com/sermons/auth/buxton/the_power_of_the_dog.htm#:~:text=The%20word%20dog%20in%20the%20Scriptures%20often%20means,only%20Son%20from%20the%20hands%20of%20wicked%20men.

That's only part true it comes from the 22nd Psalm and is one of King Davids upsetting poems where he expresses emotion about his enemies. In the most general explanation the Psalm is about a person(/in this case the person being King David) is crying out to God to save him from the torments of his enemies and in the last 10 verses thanking God first rescuing him.

The saying is referring to the 22 Psalm and is said by King David where he's crying out to God to save him from the torments of his enemies then in the last 10 or so verses thanking God for doing so..

As fatsacwins1 said, it is from 22 Psalms, verse 20.

https://www.biblegateway.com/passage/?search=Psalm%2022&version=KJV