Electric fireplaces are energy efficient because none of their energy is wasted. The light produced is used for the look of flames for a cozy appearance, and the heat offset is used to warm your home.
Make sure you look at the manufacturer's guidelines for how powerful the fireplace should be for the amount of square feet you want to heat. If you have a small, closed-in room, you'll want a smaller unit than if you have a large open-concept area that you want to heat with the electric fireplace.
Some electric fireplaces have a thermometer that allows you to set a desired temperature, and then the unit turns off when that temperature is reached. Another option allows you to shut off the heat so you can enjoy the look of the fire without the heat.