Why Fans Love Luna Lovegood
What makes her different
Luna Lovegood doesn't appear until book five, and she immediately breaks the pattern the reader has come to expect. She believes in creatures that don't exist, she says exactly what she thinks regardless of social consequences, and she doesn't seem to notice or care that other students think she's odd.
In a series where most characters are defined by their relationships to power, houses, blood status, prophecy, Luna is defined by her relationship to truth. She believes what she believes, and she doesn't need anyone else to validate it. This makes her simultaneously the strangest and the most emotionally secure character in the story.
What she represents
Luna's role is to show that there's more than one way to be brave. She's not a fighter in the traditional sense, though she does fight when it matters. Her courage is the quiet kind: she tells Harry she believes him when nobody else does, she comforts him about death more honestly than any adult in the series, and she endures months of imprisonment without losing her kindness.
She's also the character who most clearly represents the reader's relationship with fiction. Luna believes in things other people can't see, which is exactly what every reader does when they open a book and decide to care about people who don't exist.
The reason fans love her is that she gives them permission to be themselves. In a story full of characters who worry about fitting in, about being in the right house, being pure-blood, being chosen, Luna simply doesn't worry. And the story rewards her for it.