All of them are past tense "walk", so they are the same in that way. They are different in what aspect they use and what they imply about the subject.
She walked is past perfective. It implies that in the past, she walked, and that action is complete (it is not still ongoing). It makes no assumption about the habit of walking every day (which the latter part of the sentence clarifies). This sentence says she walked for a month, it was not a habitual action, and it stopped after a month.
She used to walk is past habitual. It implies that the action was part of a habit, and that habit does not exist any more.
She had been walking is past discontinuous. It implies that the result of the action was later reversed.
All three state that "she" walked to school for a month. The key differences:
Sentence 1: No habit is implied. It is simply a statement of what happened.
Sentence 2: A habit is implied, and it is also implied that the habit is now broken.
Sentence 3: It is implied that the action did occur, but no longer occurs. This may or may not be be indicative of a habit.