The baba-yaga (pronounced BAH-bah yah-GAH) is not a witch. And as you will see in this story, it is not one specific character, but rather a category. As in this tale, she may have sisters, nieces, or other relatives (no children, though). She is not an evil character, but she is very dangerous, unless one knows how to speak to her (as the hero always does). She does not have magic powers, unless one counts knowledge, or the use of magical objects, as magic. She appears in a variety of folk tales, always as the provider, willingly or not, of knowledge and of magical objects.
She plays a different role in the tales with a male hero, where she is usually a helpful character. In the tales with a female hero, she is a threatening magical entity, ready to destroy (eat, kill) the girl if she doesn’t accomplish certain tasks (or even if she does), as in this tale. The “bony leg” nickname is common, but never explained or commented on. As always in tales, this is just what Baba Yaga is.