A backlight inverter board is a common source of LCD backlight problems and can fool people into thinking their monitor is dead. The inverter works much like a battery for the LCD monitor. An inverter board powers the backlight.
The motherboard's voltage, usually a few volts, is insufficient for an LCD screen which needs a few hundred volts. If the inverter on your laptop fails, you will have trouble viewing your screen. Common signs of inverter failure include a dark screen or black screen and a "buzz" noise from the bottom of the screen.
In a nutshell, this Inverter board is the pen-sized board that is usually placed on the bottom of the LCD screen, either in the same case with the LCD screen, or above the keyboard. The inverter is one of the key parts within a display; it allows for the laptop's display to be lit by providing power to the screen's backlight.