Shortly after Hamlet follows the Ghost off stage, Horatio asks Marcellus what the Ghost's presence means and what will come of Hamlet's interaction with it. Marcellus responds by saying,
Something is rotten in the state of Denmark. (act 1, scene 4, line 95)
Marcellus's famous line indicates that he believes that something is amiss in Denmark that has motivated a tortured ghost to walk the earth and seek Prince Hamlet. His comment also alludes to Denmark's corrupt ruling class and unjust administration. Claudius has recently assassinated the king, usurped the throne, and married Gertrude.
In addition to the corrupt political hierarchy of Denmark, the rotten smell could also allude to Claudius's relationship with his brother's wife. Their relationship is something that greatly disturbs Prince Hamlet throughout the play and is an additional motivating factor to avenge his father's death.
Overall, Marcellus's comment alludes to Denmark's corrupt political hierarchy as well as Claudius's incestuous relationship with Gertrude. His comment is later emphasized when Hamlet compares Denmark to a prison, which relates to the corrupt, threatening environment of the country under Claudius's reign.