A lot of what makes the horror in Five Nights at Freddy's so good is the atmosphere and sense of absolute dread. Nothing really encapsulates that feeling quite like the mini-game in the fourth installment of the series.
The mini-game has you sitting in a hallway looking at a plush toy of the third game's antagonist Springtrap. Affectionately referred to as Plushtrap, this little beast spends his time staring you down from across the hall while sitting in a chair. The goal is to catch him on an X that's on the floor before he manages to creep up on you. Doing so reduces the difficulty of the next night by cutting hours off the clock.
Part of the fear comes from how strong the desire to win the mini game is, given how beneficial the reward is, the other part comes from having to sit in a dark room with a creature you know is slinking toward you. You can't be too hasty or too negligent, or he'll be all over you.
Here's a video from IULITM that fully encapsulates the silence and dread of the event.