Where does the phrase “something rotten in Denmark” come from and What does it mean?

The phrase “something rotten in Denmark” means: Something of a highly suspicious nature; something likely to be corrupt.

We have it from Shakespeare’s Hamlet, Act I, scene 4. Hamlet has been summoned by the ghost of his father, the murdered king of Denmark, into a conversation apart from his friends Horatio and Marcellus.

His friends urge him not to go alone, for fear of injury, but Hamlet insists and will not be denied, saying, “Unhand me, gentlemen, By heaven, I’ll make a ghost of him that lets me,” and departs with the ghost.

Marcellus then says, “Let’s follow; ’tis not fit thus to obey him.”

Horatio replies, “Have after. To what issue will this come?”

To which Marcellus responds, “Something is rotten in the state of Denmark.”