They don't generally run more efficiently, but they do run faster.

Laptops are designed to run off battery, if need be. Most people want the computer to run longer when on battery, rather than running fast and spending the battery quickly (particularly if you are working), so the laptop is designed to conserve energy by running the processor and other components in a slower low-power mode. Some even switch from a powerful graphics chip when plugged in, to a simpler graphics chip when running on battery (graphics can use lots of power).

When the laptop is plugged in, there's plenty of power and you're not worrying about the battery running out, so the laptop cranks up the speed of everything.

The thing is, it might be more efficient in the low power mode because it's going out of its way to not be wasteful (by default), and using more power might not speed it up as much as it uses more energy.