In Slavic folklore Baba Yaga is a witch or hag who kidnaps and eats small children. She flies through the air in a mortar, using a pestle to steer her way, and a silver birch broom to sweep away the tracks left behind her. She lives in a wooden cabin that stands on a giant pair of chicken legs. Her home is protected by magic, sharp teeth, and human bones. In some stories she helps people, guiding them in their quests, and in others she menaces and kidnaps. In all she is dangerous. Baba means 'grandmother' or 'old woman', and Yaga has several possible meanings: 'lazybones' or 'sluggard'; 'pain'; 'question', 'doubt' or 'quarrel'.
The wolf in question is a character from the fairytale Little Red Riding Hood. A little girl - Red Riding Hood - sets out through the woods to take a basket of food to her grandmother. On the way she meets a wolf, who questions her as to her task, and suggests that she stop to pick some flowers. The wolf then gets to the grandmother's house first, eats her, and puts on her clothes and climbs into her bed. When Red Riding Hood arrives he pretends to be the grandmother, but Little Red exclaims "What big teeth you have!" at which the wolf replies "All the better to eat you with!" and swallows her whole. In most modern versions of the tale, Little Red and her grandmother are rescued by a passing hunter who cuts the wolf open and pulls them out.