On the night when Hamlet meets the ghost of his father, there's a party going on at Elsinore. It seems that the whole court's turned out to get blind drunk, but it's Claudius who's the center of attention. The custom at such boozy gatherings is for the kettle-drum and the trumpets to announce when Claudius has drunk down all his wine. Hamlet is throughly disgusted with this, not least because he's still brooding over the death of his father and hates to see anyone else having a good time, especially Claudius.
Hamlet tells Horatio that it is a custom "more honor'd in the breach than the observance," meaning that it would be more honorable to break this custom of drunken revelry than to observe it. The riotous celebrations are doubly offensive to Hamlet as they appear to confirm his conviction that "something is rotten in the state of Denmark,"—though it's actually Marcellus who speaks that line—that the whole kingdom's become noticeably more corrupt in its morals since Claudius came to the throne.