What does the energy saving switch do on my led lit lcd tv?

When you shut the set off it's in standby. That means the set still has a 5 volt line that keeps the TV's memory. The switch is for killing the power to the hole set. You'll notice you usually have a standby light. Flip the switch and it kills ALL power to the set. Not even the standby light is on. It's the equivalent of unplugging the set.
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Energy Saving LED Lighting