This song is about a paranoid man who is convinced that his dreams are being monitored, and it's driving him insane. No matter what he does, the "Dream Police" are always inside his head and waiting to arrest him.
Unlike the paranoia of, say, Black Sabbath
, this song has a comedic element. Like most Cheap Trick songs, it was written by their guitarist Rick Nielsen, who creates lots of offbeat characters for his compositions, which keeps it in good fun.