The film uses a narrative that subverts from normal linear narratives. I would like to know why this is and what effect it has.
Why is this non-linear narration?
As the protagonist name goes by Nemo Nobody, we're talking about nobody in the film. Nobody we see on screen exists in Nobody's life-yet. Infact there was a particular scene(few minutes before the climax) when 118 year old Nemo says
In chess, there is a move called Zugzwang ...when the only viable move is to not move at all.
That's where the story's gist is being revealed. Whatever the viewers have been seeing right from the beginning to the very point ,have never happened at all,atleast not yet. Nemo at 9 year old was confused to make a choice.He wonders whether he has to stay with his dad or go along with mom.Then he goes on thinking what would happen to each and every choices that he would make. He imagines all the possible combinations.
Goes with mom. Meets and falls in love with Anna at 15.only to miss and find her again at 20 something.Makes love with her and Anna leaves. They find each other again(damn,Butterfly effect). They get married.Some year later, the car in which Nemo travels is met with an accident. He drowns and dies. (Butterfly effect again)
Stays back with dad.Meets and falls in love with Eisle. Here some sub cases:
1) Eisle rejects him for Stefano(the man she desires). So Nemo finds Jean, falls in love with her, marries and becomes rich but unhappy. Later was assassinated.
2) Eisle was somehow convinced and Nemo finally get her to marry him. Here, he imagines the car which carries them after marriage explodes due to an accident and he lives with Eisle's memory and aeons later goes to Mars to fulfil Eisle's earlier wish of- to bury her ashes in Mars and there he meets Anna again. Well, even here he dies due to sudden explosion(oh no. Not again)
or rather he likes to imagine where their marriage car doesn't meet with any explosion but their marriage broke due to Eisle's depression and kind of guilt. One day after Eisle leaves him, he dies by drowning himself due to some unsaid, unseen Holocaust where water drowns his whole home. (should have learnt swimming properly when you were 9, Nemo instead of peeking at Anna -_-)
All of these are might happen cases of Nemo's imaginations. Now,back at 9, he wonders what choice to make. Which choice would lead to what life? He thinks all the possible scenarios as a 9 year old while chasing his mommy behind a train (all these happens in movies, meh!). That's when Nemo makes a decision.
Every path is the right path. Everything could have been anything else and it would have just much meaning.
As said by 118 year old Nemo.
So, since at the end Everyone dies in all of his 'may be possible scenarios', he runs in the middle track (neither back to his dad nor behind his mommy) concluding as long as he makes a choice, anything and everything might be possible.
What effect did it had?
I can just talk about myself but not everyone. Probably, the director wants to see this movie in the eyes of 9 year old Nemo which indeed made it an unforgettable experience. The non-linear narration is partially to keep the viewers hooked to their seats with 'WTH is happening now and which is true' thoughts and partially to show how a 9 year old is learning about making choices and it's effects. Though the movie was said to be based on The Butterfly fly effect, I highly disagree with the crew as it gives a false picture of it. They described the Butterfly effect just as in definition but gave really bad examples to it.
But nonetheless, it was one of the most Wonderful movies. I thought to show it to my little brother saying 'As long as one makes choices, nothing can be predicted and our well-being depends more on the choices we make than anything else'. But the movie is R-rated and after completely watching it, I decided not to show that movie to my baby bro for obvious reasons(-_-). May be Nobody would tell us that. We have to find it ourselves-The importance of making choices.
Well, for me personally, it is more interesting to follow a movie that deviates from the normal linear timeline, jumps back and forth in time. It makes me more curious about the story line, more included, and it makes me follow the story more carefully. So, I even kinda prefer this kind of story telling to the usual, "normal" way.. This approach is not used only in the movie industry (e.g. Mr.Nobody, Memento). It's shown as very effective in series (e.g. Lost), and novels (e.g. The Witcher), too.