I don't understand what Dumbledore sees in the Mirror of Erised?

Question

Does he see his sister and parents in there?

Answer 1

He regrets what happened to his sister, so he probably sees everything being "OK again"

Answer 2

Yes, I think he does. He sees that his sister was never killed in that fight. He sees that his parents are both alive and happy. I think he sees Aberforth not angry with him. And most of all, I think he sees his best friend, Grindelwald, not being an evil wizard, back together again.

Because his worst memory was his sister's death, so I assume that his biggest desire would be for her to live.

Answer 3

Yes he does, he sees his whole live, fully healthy, happy family together. J.K mentioned in the first book, when Dumbledore tells Harry what he sees, he lied, he didn't want to tell an 11 year old what troubles he has done, Dumbledore believed that Harry was too young to bare another burden, in which was that the greatest wizard was flawed. Dumbledore was wise, if he hadn't done that, Harry could've easily strayed to dark arts, or anything worse than that.

One thing Dumbledore longs, is to be free of the burden he carries, he feels responsible of his sister's death, it was him who caused it, when Grindelwald and him had a row at each other, and caused his sister's death. This is told to us in the last book.  

Answer 4

I think it may have been JK Rowling who said that deepest desire of his heart is that he did not inadvertently cause his sister's death.  He probably sees her alive and well, or maybe sees his life without ever meeting Grindelwald at all.  If it wasn't Rowling that said that, it is what is pretty commonly believed.