Computations, statistics, logs, networking, emergencies aren't impacted by low power modes. They continue as usual.
 
Map
 
 
Display fade
When not moving, when you haven't used the buttons for a while, when the battery level nears 0%, Motion will first dim its backlight to lower its power consumption.

To wake it up, press any button.
 
 
 
Display off
When left idling longer, Motion will shut the display down completely to further improve power consumption.

To wake it up, press any button.
 
Putting it in low-power mode yourself
You can put it to sleep yourself by pressing both the upper-right and lower-left buttons. This function loops between "day mode", "night mode" and "low power mode".