This passage was written in a rural and older dialect of English, which can make it tricky. In this case, hern is a way to say "belonging to her," or "hers." It follows the same pattern as "mine," by adding an -n to the regular possessive pronoun to make it an object.
This isn't part of Standardized American English, just as "ain't" isn't, but it is part of a dialect, an alternate grammatical system that follows different rules. The writer is emphasizing the speaker's identity as a dialect speaker by using words like "hern" and "ain't," and also by spelling to approximate the sound, like "ter" instead of "to." It's meant to make the dialogue more vivid and the character seem more naive and charming.
Miss Polly probably wears her hair in a tight bun or ponytail and dresses in a severe, old-fashioned or masculine manner. "If she let down that tight hair of hers, and let it flow loosely, along with wearing fashionable hats and feminine dresses, she would look quite pretty. Understand, she is actually young."