Sometimes in a game you need to do some things that some of the PCs know about, but that other PCs really don't know about, mainly because the characters are not present in the scene in question. You can do this with all of the players knowing what's happening, but this relies on their ability to keep player knowledge separate from character knowledge. And then sometimes you want things to be a genuine surprise to the players, as well as their characters.
In such situations, the usual thing to do is ask some of the players to leave the room for a while, or take a subset of the players aside into another room for a bit. If you thought passing notes to players was a good way to ramp up the paranoia, you ain't seen nothing yet.
In practice, this procedure should be limited to extreme circumstances, and the separate sessions kept short and sweet to avoid boredom in the unattended group.
On the other hand, we've seen games in which two different groups of PCs are being run through an adventure simultaneously, with a single GM running back and forth between rooms. The two groups don't know anything about what the other group is doing until they run into one another, at which point the sessions can be combined. Just a warning: the GM's job scales roughly as the number of separate groups squared. And the number of game-interrupting outbreaks of irrelevant conversation, Monty Python quotations, and people deciding to play Nintendo instead of the actual game scales roughly exponentially.
Transcript
{Padmé's funeral on Naboo}
GM: Right, with Padmé's funeral done, can you guys leave the room for a bit? We have a small private scene to conclude.
{The lava bank}
GM: Okay Annie, it's a few days later on the other side of Naboo. The lava is still cooling down and Anakin is clutching grimly to life on the smoking bank.
Anakin: This is not real. This pain is not real. This heat is not real.
Anakin: Obi-Wan, are you still there?
Anakin: These tears are not real.
Anakin: I didn't mean for any of this to happen.
Anakin: Trust me.
Anakin: Love will prevail...
Anakin: Padmé... Padmé...
{Anakin's voice trails off slowly}
Anakin: Padmé... Padmé...
Anakin: Padmé...
Anakin: Padmé...
Anakin: Padmé...