The bulb is an integral part of the flame effects inside an electric fireplace. Without this light source the flames can’t be displayed.
You can tell whether the bulb has blown because you can still hear the motor operating inside the fireplace but nothing is being displayed.
We have a guide on how to change the bulb in an electric fireplace here.
A blown bulb may not be an issue for all types of electric fireplace.
Many newer models of electric fireplace (like ours) use LEDs rather than bulbs, which are rated to last for a much longer period of time and are likely to last for many tens of thousands of hours of operation.
If your electric fireplace uses LEDs rather than halogen bulbs and your flames aren’t working then there may be another issue with the fireplace.