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.
The inverter powers the backlight on your LCD monitor. 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 monitor 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.
The average person can install a new inverter board themselves. On standalone monitors, you pry open the monitor case with a screwdriver. On a laptop, unscrew the bezels in the corner. Some find this process easier because you only switch the input/output cables and do not need new drivers.