I think that it was the same for everyone, once we started to watch this series. I just thought "Why is Jintan's father talking while Menma is doing the same?", and only in a second moment I understood why: she was already dead. That was a little shocking for me, but I realized that the only person who could see her was Jintan, one of her precious childhood friends.
We figure out that, in fact, Menma died when she was young and she is there because she has a wish that she has to fulfill before she can reach Nirvana. At the begin it will be only Jintan the one who will help her because the other don't believe in his words and in Menma's ghost existence; but piece by piece everyone will understand how strange is the matter and will believe in Jintan words (even because Menma will start to write in her diary that was kept in their secret base, the one they uses when they were child and called themselves Super Peace Busters).
Though her body has grown a bit, Menma's personality is always the same as when she was a child. She's easy-going, reckless, sweet, kind and especially, she likes to play and loves her friends. Since she was little, she was the kind of person that smiled even if things were difficult. If was even because of this that everyone had some regrets when she passed away, especially Jintan who thought to be the culprit of her death.
As time went on, Menma tried to do her best and to let the other feel her presence when they were together. She really wanted to see her group of friends together again, and she tried hard in order to do so. Sometimes it happened that she remembered something about her past, and once she recalled some memories of Jintan's mother (who died before her time). She told her that Jintan always tried to be strong and so he didn't cry in order to don't make his parents worrying. But that was the point that worried his mother the most, and Menma promised her she would do her best to work him off, as she will do at the end of the series. She tried to cook the coockies that Jintan's mother was used to do in order to please him.
When she realized that she's about to disappear, she writes some notes to each one of her friends, and as if playing hide and seek, they all see Menma disappearing at dawn, while expressing their feelings of love for her. In Jintan's note there was even written that she wanted to become his wife... baaaw... When she finally reaches Nirvana, everything gets better for all her friends, as if they could start a new life carrying her memories in their hearts.