Connotation is a secondary or associated understanding of a word or phrase. For example, the word religion can carry a number of diverse connotations for a lot of people. Some people might feel religion connotes warmth, affection, and family. Others might think it connotes ignorance and bigotry.
Denotation on the other hand is simply the actual definition of a word. For example: Dalmatian. It's a breed of dog that is white with black spots. For some people the word "dalmation" might have a connotation, like that they are the dogs that are always with firemen.
Speaking of firemen, Fahrenheit 451 is a book about firemen. Right from the outset, the reader recognizes that the denotation of firemen is people that put out fires. The connotation is that firemen are "good guys" that are brave, strong, and selfless. They help old ladies and rescue cats out of trees.
Bradbury flips all of that on its head when he tells the reader that firemen are in charge of destroying books by burning them. Firemen are not brave and selfless wonderful people. In Fahrenheit 451, the firemen are the antagonists of learning and knowledge.
Throughout the novel, Fahrenheit 451 denotes the temperature at which books burn: this is a simple, objective fact. Additionally, though, book burning carries an emotional or connotative meaning. For the audience reading the book in 1953, the year it was published, book burning would have brought back frightening memories of nighttime bonfires of forbidden texts in Nazi Germany. Book burning was not simply an objective fact, but stood for tyranny, totalitarianism, and the loss of freedom: audiences would have brought to this reading a terrified understanding of the repressive society Bradbury was depicting.
The name Clarisse, denotatively, is simply the name of a character; denotatively, it also means light and bright, but these words hold an emotional or connotative resonance that is especially important in this novel about burning. The name represents a different kind of light or fire than the hot, destructive fire that Montag uses to burn books. It is a soft, illuminating light that awakens Montag's soul: on page three, Clarisse is described as follows:
Her face, turned to him now, was fragile milk crystal with a soft and constant light in it. It was not the hysterical light of electricity but-what? But the strangely comfortable and rare and gently flattering light of the candle.
The word "cobra" on page six to describe the stomach pump is also connotative. Objectively, a cobra is just a snake and the word, on one level, simply describes the long, narrow quality of the tube put into Mildred's stomach. The word "cobra" also carries the connotation of a dangerous animal that will strike out unexpectedly with sharp fangs to bite and poison a person. Thus, even a hospital, normally a place of healing, is described with ominous overtones, contributing to the novel's dystopic mood.
The word "hound" also has connotative meanings. Denotatively, the hound in the novel is just a machine that the firemen use to help fight enemies, but the word "hound" itself carries the alternate meaning of harass, and its emotional resonances go even deeper than that: hounds historically are used en masse in hunts against a single, helpless creature like a hare. The mechanical hound in this story is not simply a tool of law enforcement, but rather a malevolent creature who adds to the dystopic quality of the novel. On page 11, the Hound is described as
like a great bee come home from some field where the honey is full of poison wildness, of insanity and nightmare, its body crammed with that over-rich nectar and now it was sleeping the evil out of itself.
Bradbury could have as easily created a mechanical killing poodle, but the word "poodle" would not have carried the same connotation as hound.