What is an inverter board?

"inverter" has many uses, but here I think you mean a circuit to convert one DC voltage to another by INVERTING the input DC to AC, running thru a transformer, rectifier, regulator to output the new DC voltage. When used in context as an "inverter board" it refers to the backlight of an LCD screen. It is the board(s) that the backlight(s) is mounted on.