Dumbledore says:
"It does not do to dwell on dreams and forget to live, remember that. It shows us, not our deepest desires, but rather, our hearts' deepest needs. "
In Harry's case, he sees his parents alive and well, surrounded by his friends and family. He doesn't see himself as the most powerful wizard in the world or having vast riches. This is because his deepest need is love and family, which he lost at a young age.