Why are certain wattages of light bulbs brighter than others?
Light is radiated power; Power is not just a mechanical thing.
Take the old incandescent bulbs. The electricity does work to heat the filament, causing it to radiate energy as light. That would cool it down again, so more electricity has to be used all the time to keep it hot. The rate of using electrical energy is power.
Light is a form of energy (work). The more light you want, the more/ faster electrical energy you have to convert into light energy.
More power enables you to heat a tungsten filament of greater dimension (in length or thickness)---to the same glowing temperature---so with more radiating surface, you have more light. More light = greater brightness.
Or heat the same size filament to a higher temperature, thus creating a larger portion of the radiated light in the visible spectrum (e.g. halogen bulbs).
Separate names with a comma.