The players have to constantly adlib and adapt to plot developments. If they become overwhelmed, it is "in character" to stop and discuss the situation with each other. The Game Master on the other hand has no confidants. He is expected to react instantly to what the players describe their characters doing.
The typical GM spends hours preparing before a game; planning for everything the characters might try. But no matter how much you prepare, the only sure bet is that the players will think of something you didn't. In fact the more material you prepare, the more likely it is that one of the players will latch on to an incidental detail and take off in an unexpected direction faster than you can say "Red Herring."
Every Game Master has his own style. But all of them need to be able to think on their feet. Improvising during a game is easier if you are ready to step away from the written game and go in the direction the players want to try. Remember the player characters are the main characters in the story you are telling. By definition the plot is what they do, not what you planned for them. You want to gently guide the group 'back on track' without letting them realize that they ever deviated from the script.
There are three techniques which can improve your improvisation behind the GM screen: Plot Seeds, Stock Characters, and Rakugo Props. (On a personal note: Some of the best games I've ever run, I've shown up at the table armed only with this bag of tricks and no fore planning to get in the way.)