If you haven't been working with layers yet, you are on a different level with all of the other designers in your field. Layers can be dynamic, beautiful and engaging elements that grab a hold of your viewers. So why wouldn't you use them?
As stated earlier, it's an eye catcher. It can really add depth to a piece and turn "pretty" into "interesting."
It's not to hard to do and a lot of programs carry this option.
It can be used to incorporate two different ideas into one graphic. For instance, you could take 7 United States flags and drop them into an outline of a star. Each flag can even be a different opacity.
It will increase memory size. Not too much though. You won't be able to see any differences in work flow unless you are using a 386. That's old PC humor...
Printing different shades of colors is different than what you see on the computer screen. But then again, a lot of print jobs hit this speed bump.
So how is it done? The concept is really simple. Imagine you have a projector; the old projectors that were used in schools back in the 1980s and 1990s. They all used plastic "films" which projected an image on the white screen using light. These films had images with certain opacity levels to let the light through.
In theory, this is the same as using layers. Layers are much like the "films" and can have different effects added to them and properties as well. Photoshop offers a lot of special effects and layer blending modes. Most Adobe software programs have layer options, even After Effects uses them.
Once you have the layers concept you can move on to layer effects and blending modes. This will change what you are able to do in Photoshop. Adding a gradient to a graphic layered on top of a background will look amazing if done correctly. In summary: learn what you can and practice layers. And do it often.