A fan controller is simply a tool that controls the voltage of a device in your computer, usually a computer case fan or a CPU cooling fan. By turning down the voltage on the fan, the fan spins slower and makes less noise. If you have a noisy case fan, you may be able to silence the fan by adding a fan controller to the fan.
Fan controllers, whether controlling single or multiple fans, can simply control the fan speed, or in some cases they can monitor the temperature of the fan and various locations inside your PC. Use of a front-mounted fan controller with temperature monitoring allows the quiet computer user to produce the quietest computer possible while still maintaining a sufficiently cool environment for their computer components.