What does FG stand for?

FG stands for Frequency Generator (or Feedback Generator), it has an output with a frequency proportional to the fans speed. It is used by the CPU to determine the fans speed.

Some (older) fans have an extra winding internally and the FG signal is a sinusoid with both amplitude and frequency proportional to fan speed.

Modern fans almost exclusively use a Hall-Effect sensor and the signal is an open-collector square-wave signal where the frequency is proportional to fan speed. Peak voltage is determined by the magnitude of the power supply that feeds the pull-up resistor.

Be careful. I seen AC-DC power suppliers labeling "FG" for the frame ground. That means, attaching to the metal of the device.