Someone has no reason to be afraid of one; someone should not be shy about approaching or talking to one. Don't worry, child, I won't bite. I just wanted to give you a message to pass along to your father. This is your Uncle Jack, son. Well, go on and shake his hand, he won't bite you.

Is not threatening or does not need to be a subject of caution; is friendly. The phrase is typically used as an assurance to a child who is wary of something or someone. You can ask Mr. Caruthers. Go on, he won't bite. Hi there, what's your name? Don't worry, I won't bite!