Passing notes to players is a convenient way of informing a player about something that their character knows, but which none of the other characters know. This leaves it up to that player whether or not their character reveals this information - and how much of the information - to the rest of the party. This makes for more realistic roleplaying.

It also incidentally ramps up the paranoia level of experienced gamers to incredible levels. Less experienced gamers may not realise this side-effect, assuming that note-passing is a simple and logical way to communicate relevant information. If you have the right mix of gamers, this can cause some interesting interactions.

Transcript

GM: Annie, can you please read this note?
{Anakin has nightmare}
{Anakin stands on balcony}
{Padmé emerges, goes to leave him alone}
Anakin: Don't go. Your presence is soothing.
Padmé: What are you doing?
Anakin: I had a nightmare, about my mother. I fear she is in terrible danger.
Padmé: Wow. If she's in danger, it must be really bad. We could go and help her.
Anakin: No. I'll be thrown out of the Jedi order if we abandon our mission.
Padmé: We'll arrest Bubble and get the Peace Moon plans off him first.
Anakin: We can't do that. There's no evidence to implicate him.
{beat}
Anakin: This is a case of family versus duty. What do you think is more important?
Padmé: Whatever gets the most...
Padmé: No, wait. Family!
Anakin: You're saying we should ignore the fate of the Republic to save my mother?
Padmé: Yes!
Anakin: That's very brave of you, Senator.
Padmé: I don't ever want to take sides with anyone against the Family.