When I turn down the brightness of the screen on a Samsung Galaxy Mega am I lowering power consumption or increasing the opacity of the screen?
I'm going to answer generally, since the same is true of any smartphone. There are broadly two kinds of colour screen used on mobile devices (smartphones, tablets, wearables, and handheld game consoles): LCDs, and OLEDs.
These change their opacity according to an electrical signal. But to see that change in opacity, they need a source of illumination: a backlight. In early PDAs and the first few generations of Android phones, CFLs (which are basically small fluorescent tubes) were used for backlights, but these days many LCD screens are lit by white LEDs. Either way, the brightness slider controls how bright the backlight is by varying the voltage to it, so it directly affects power consumption, just like a dimmer control on a lamp.
It used to be the case that LCDs used a lot more power to be opaque, so displaying a black screen drew more power than displaying a white screen. However, manufacturing techniques and densities changed a few years ago, and the difference is negligible these days.
OLEDs are a new kind of LED. They can be a lot smaller than traditional semiconductor LEDs: small enough for each pixel to be a separate LED. There's no need for a separate backlight. Because of this, the brightness slider multiplies the brightness of every pixel separately. Decreasing the brightness setting doesn't decrease power consumption directly. The power consumption of the screen depends on how bright is the actual image it's displaying. In general, decreasing the brightness slider will tend to decrease power consumption, because the screen is darker overall, but a white screen on minimum brightness will draw more power than a black screen on maximum brightness.
Some phones with OLED screens have software that adjusts the brightness dynamically, instead of simply multiplying the screen colours by a constant value. This increases the brightness of the bright colours when more of the screen is dark, and decreases the brightness when more of the screen is bright, so the overall brightness looks the same. This can help save power: when you've adjusted the brightness so darks are clear in your environment, there's no point in the phone burning more power to make the brights look brighter than you need. On Samsung phones with OLED screens, you can find this in the Display settings, labelled Auto adjust screen tone.
Whatever type of display technology your phone uses, decreasing the brightness control can use less power, but for different reasons in each case.
Lowering screen brightness is one of the energy-saving tips always coming out on top. That's not even specific to your Samsung Galaxy Mega, but valid for all devices. For other tips (and more details), see e.g. What can I do to increase battery life on my Android device?