His appearance in the films, is extremely disfigured to represent how he burnt to death, and he always wears a fedora, a green and red striped jumper and his razor gloves which he uses to kill (although in the 2010 remake, he actually has blades coming out of his hands). The comedy aspect of the films comes in the form of his witty remarks and one liners that have become iconic in horror films.
In the original 6 films, his background was that he was conceived through rape while his mother worked at a psychiatric hospital and as a child, he was adopted by an abusive alcoholic called Mr. Underwood who taught him to torture animals and himself, and was often taunted by other children for being the "son of 100 maniacs" giving him motivation to go on a killing spree of children later. However, when their parents found out he was the murderer, they burnt him alive in the boiler room of the power station, at which point 'Dream Demons' gave him the option to become immortal in exchange for become their agent. From this point on, Freddy Kreuger is immortal and all powerful in the dream landscape of teenagers dreams who when he kills in the dreams, die in real life also. The idea for this is said to be influenced by a spate of Sudden Unexpected Nocturnal Death Syndrome that happened around the time before the screenplay was written.
Freddy's powers in the dream world include being able to manipulate the surroundings and control it in general which adds terror to the teenagers last moments as he hunts them. His power heightens the more people know and fear him (and also due to the amount of souls he absorbs). Often a childlike playground rhyme is chanted by people in the dream to warn the teenagers of his presence. In some cases, he can escape from the dreams into the real world, where although still supernaturally strong, he can be defeated. The film's often are centred around one main teenager, usually a girl, who defeats him in the end although the end is always left often to allow sequels to be made e.t.c. also this adds fear as you're never quite sure if he's actually defeated or not and this ambiguity scares the audience.