It should be "She didn't know any better." (though sometimes even native speakers say "no better", it is grammatically incorrect). It means that she didn't something wrong, but she didn't do it to be bad or mean. She simply had never learned to proper way to act, and therefore she should be more easily forgiven for what she did wrong.

Meaning she did something wrong but was unaware of the consequences of her actions. Like a small child breaking something unintentionally.