What does the Power Save option do on 3DS consoles?

Solution 1:

They talked about the Power Save mode of the first 3DS during an "Iwata Asks" session:

Employing a technology called "active backlight," this feature "precisely controls the brightness of the backlight according to the brightness of the screen being displayed," Umezu explained. "When the screen as a whole is dark, the backlight itself gets darker, which saves power."

And about the battery-time you would save:

The energy savings offered by the power save mode should make it a requisite for every 3DS player. "With the backlight set to the brightest level and the power save mode turned off, battery duration was about three hours," Umezu said. "But if you use the power save mode under the same conditions, it gets about 10–20 percent longer."

(From Joystiq)