At the end of the 2-part first season opener, Friendship Is Magic, Nightmare Moon is turned into Luna. Her appearance as Luna is like any of the other regular ponies. In the season 2 episode Lesson Zero, Luna returns, but now has an appearance very similar to Princess Celestia. She's taller than other ponies, and her hair is constantly flowing, with sparkles. This change in appearance wasn't discussed during the episode, have the show-runners explained this anywhere?
Lauren Faust gives an unofficial explanation shown here, but we don't have an official one. She says:
When Nightmare Moon was defeated, her evil power was eradicated. Luna was reborn with her magic levels very low. It took time for her "good" power to come back to her, and now she's healed, reformed and rehabilitated and it's indicated by her magic mane
It should probably also be noted that in the latest episode Luna also demonstrated transformative/illusion magic some of the times she frightened the other ponies, so it's also possible she merely choose to appear this way; One reason to do so would be to look more like her sister.
As seen with Twilight over the episodes from sn 3 on, when normal ponies turn into princesses they turn into Alicorns which have a different path of growth to separate them from regular ponies. Alicorns change to have longer horns, larger wings, more slender bodies and the final sparkly flowing mane. My guess is this: Luna wasn't officially a princess as she is referred to as Celestia's sister and not a princess so when she was freed of the nightmare moon thing she went back to being her old self; an Alicorn but not quite a fully developed one. She was then offered the title of princess which completed her transformation to full Alicorn status.
I think, heck, she hit puberty. Or she matured. Or to make people less afraid of her she changed her appearance to look like her sister since every one loves Celestia. Or maybe there is changes when you are a Princess. Because if you compare all 4 you will see that they grow taller and their hair changes.