"Snake" was Cara's name for the Mord-Sith who trained her. Cara called her this because when she first saw Snake, it was when she had come to where Cara lived to take her as a Mord-Sith. Cara hesitated when her father told her to stab Snake with a knife, and Snake smiled at her and told her that her hesitation had made her Mord-Sith. Cara compared her smile to that of a snake, and she called her trainer that from then on.
Since Cara's hesitation, Snake always reminded her not to hesitate because of the memories of what she could have done had she not hesitated that Snake's words brought back. For example, when Cara tried to keep rats in her bedoom from biting her by leaving them her dinner, Snake told her, "Don't hesitate, Cara, or the rats will get your dinner." Also, when Cara was about to begin the last step of her training - the training and killing of her father - Snake told her not to hesitate. Cara obeyed her despite her father's pleading, which shows how effective Snake's words were.