the inverter powers the backlight, which is traditionally a ccfl. Think of it as a ballast and dc-ac inverter in one. The laptop supplies dc voltage, and the inverter "inverts" the power to ac for use to power the backlight.
the backlight is typically a fluorescent tub inside the lcd panel. typically hard to get to and may include removing the light guide, diffusers, logic boards, and possibly breaking welds on the frame.
Now, for something easy I can recommend is to check your lcd switch. Usually it is a little plastic switch near an lcd hinge, or a little rubber nub that gets pressed when the lid is closed. if this is stuck down, then the backlight will not work. try cleaning it with a stiff bristle brush.
also never rule out your funtion keys, FN+arrow keys or Fn+F6.
if the switch is not the issue, nor the keys then it could be either the inverter of the lcd. inverters are typically easy to replace, however you run the risk of breaking your lcd bezel. lcd panels are also easy but require more screws, and sometimes you must carefully seat and route cables.
also consider that sometimes the mainboard can cause this as well since the mainboard supplies all power to the inverter. this is not common, but can happen.
