A Boston Terrier puppy is a bundle of playful energy, and puppies often play by using their mouths to grab things--toys, rawhide bones... your hand!
These people-motivated dogs like to play and bite at your hand or ankle to get your attention and let you know they want to play some more. Most puppies tend to be “mouthy” as their teeth come in, and because your Boston Terrier does not have opposable thumbs, his mouth is his best option for grabbing onto something, or someone!
Boston Terriers tend to be a particularly “mouthy” breed. In a puppy this behavior is not generally meant to show aggression as much as it is a means of interacting with you, however, what is cute in a puppy will not be cute as your Boston Terrier gets older and biting becomes harder and more difficult to stop. Even a small dog like a Boston Terrier can cause injury if they bite, especially on delicate skin or on extremities like the hand or ankle. Teaching your Boston Terrier good manners, which include not biting or nipping even in play will serve you and your dog well in the future. It is a lot easier to guide a puppy not to nip and bite during play than an older dog that has established this behavior as a way of getting what he wants.
Make sure everyone in your household, as well as visitors, are aware of your “no tolerance for biting” policy, to maintain consistency and avoid inadvertently reinforcing biting. You will need chew toys to redirect your Boston Terrier's biting behavior to a more appropriate target. You can use a deterrent like bitter spray as well to discourage biting in your Boston Terrier puppy. Always make sure you use something pet appreciate that will not make your dog sick. Appropriate products are available from pet supply stores. Remember to be patient and firm to direct your young dog.