Dogs don't have the use of language like humans do -- but they do communicate through vocal noises, with dogs, humans and other species. Because growling can mean different things in different situations, it's important to know your dog's behavior and personality.
Growling as a Request
Sometimes a dog growls to request things from his owner. This is largely a learned behavior. If a puppy wants to play and growls at you, and you grant his request, the dog has learned that growling results in reward. The best way to address growling in this situation is to ignore the dog's request.
Growling to Protect
Dogs sometimes growl to protect things they consider their property. For example, a dog who finds a bone may growl at you for trying to take it away. Similarly, a mother may be protective of her pups and growl at other dogs who come near them. A dog may growl at the mailman thinking he is protecting you. This type of growl is a territorial warning and is the dog's way of expressing boundaries or ownership.
Growling to Express Fear
Much as young children cry or scream when they're afraid, dogs growl when they encounter perceived danger. A classic example is the dog who growls at the groomer or vet. If the dog believes the vet is going to hurt her, she warns him of her discomfort by growling. A dog who has had a bad experience with children and later growls at all kids is expressing fear.
Growling During Play
Dogs often growl while they play with one another. This is similar to the predatory growl some breeds exhibit when chasing game. It is usually not aggressive as much as it is an expression of dominance. Dogs will sometimes growl when playing with humans. This is a situational growl and shouldn't be considered a problem unless the dog also behaves aggressively by showing teeth or nipping.