"Power save" mode in electronics is a way to conserve energy or battery life when the item is left on but not in use. In the context of a monitor, this means the display is temporarily turned off until a user presses a key or moves the mouse.
In Windows, there is a configurable power-saving option to help users minimize power consumption. By going to the Control Panel or screen saver configuration screen, one can configure the number of minutes before turning off or dimming the display. According to Microsoft, one can access the power plan configuration by going to the Start menu, then Control Panel, then System and Security, then Power Options, then Change Plan Settings.
In a Mac, the timer determining how long the display remains off can be configured using Energy Saver, which is accessed on a Mac by pressing Command-Space, then typing in "Energy Saver" as search criteria.