Refer to the attached figure. It shows a simplified configuration of the typical PLL as it might be used to generate a frequency. As you can see it has the typical blocks including a VCO, a phase detector and a loop filter. these are the essential elements of any PLL. If you wanted to generate a frequency, you would take the output from the VCO and you would provide a stable reference frequency input from a crystal oscillator.
If we want to use it as a FM demodulator we remove the crystal reference oscillator and instead we feed the modulated carrier (the signal we want to demodulate from) into the reference input. We ignore the VCO output completely as it is not used. When the VCO phase locks to the incoming frequency connected to the reference input then we can take the output of the loop filter and connect it to an audio amplifier and this is our demodulated FM signal. That's how to make it work as an FM demodulator.
As you may be able to see, in any PLL, the VCO is made to track the frequency of the reference as long as the rate of change of frequency is within the loop filter bandwidth. So, when we lock the VCO to the incoming signal, the output of the loop filter is moving up and down to make sure that the VCO frequency tracks the reference. The VCO frequency modulation and the incoming frequency modulation end up matching.