In my creative journey, I started as comic book fan, drew super heroes through out high school, attended college for industrial design, never gave up on comics, worked creating toy presentations, switched to storyboards, taught english( in japan), sidestepped into graphic design(I was inspired in Japan), directed photoshoots(lots of them for home depot), managed a creative team as an art director(I hocked pool products and loved it), and even working on the animated show on the FX network, Archer.

So.. when I ask "what is design", I definitely see this from more than one viewpoint.. But I have to admit, the time that I "really" learned about design was in college, and from a specific professor, and at a very specific moment..  It was the moment when "I got it".

It was the moment when I understood that design wasn't "arbitrary", and I realized there is a way to do it right, and a way to get it wrong.

But defining design is almost like explaining light.. There is a particle theory of light, where it might have mass and behave somewhat like and object. And then there's a wave theory of light where is seen more as a force behaving very differently than an object.

I think design is very similar in explanation. Design can be described in a functional sense, or it can be seen as an artistic endeavor.  It works beautifully both ways.

I've danced a two step around the main question long enough. When you take away the photoshop filters, remove the perfumed magazine pages, de-power the powerhouse computers, and just work with basic shapes, letters, and textures, etc...

Design is the visual arrangement of elements to elicit thoughts and/or emotions.

This true for whatever kind of medium you're using; graphic design, fine art.... I think this is the bare bones of it.. And I thinks it's essential to understand this so that you know what it is you are trying to accomplish as a designer, and also what tools you have at your disposal in the design process. 

And a design can be judged by how well it brings out the thoughts or emotions in it's audience- compared to reaction the designer intended.