Libby101a offered some good advice.
Many puppies and dogs bite as a part of play. When they play with other dogs and bite too hard, the other dog will yelp and turn away, and this teaches the dog bite inhibition. I have seen some dog trainers emulate this behavior to discourage biting.
Some breeds are more nippy than others. Herding breeds are breed to nip the back legs of sheep and cows, and sometimes this instinct is triggered with humans, too.
You might also try redirecting the biting behavior by playing tug.