The TL431 is widely used at Switch Mode Power Supply (SMPS) circuits, when it is a isolated converter and the feedback comes from a optocoupler. You need to compare the output voltage to some known value so you know when to turn on the optocoupler.
PIC MCUs come with internal references, so you don't need an external IC like the TL431. But let's say you are using another MCU that doesn't come with internal references, and you want to have an AD reference different of VCC. You should use a TL431 connected to the AD reference pin, so your conversions will have a very accurate reference.
Another possible application is, for example, if you want to make a constant current source with a transistor and an input voltage that varies between 8 and 10V. In order to make a current source with a transistor, you need a fixed voltage at the base. If you use only a resistor divider, this voltage at the base will vary with this 2 V ripple at the input. You could use a zener diode at the base to fix the voltage you need, but let's say that there's no commercial zener diode for the voltage you want. You could try so a TL431, and have any voltage you want by adjusting two resistors.