This is a great question! It's broad though, so expect answers to be equally so.
How can you objectively explain the reason behind the the intuitive decisions that you make in graphic design?
This is probably one of the deepest questions that one can ask about graphic design, and it takes some serious thought to answer properly, which makes it a great topic.
I'm not going to give you a website or resource, but rather explain it to you my self. In fact, that website that you're thinking of might be the one you're on right now!
Edit: The scope of this question.
Now, this question is too broad to be fully, completely answered in this format, but because I like this kind of question, and the community decided to up-vote it rather than closing it, I'm going to provide an answer by explaining some examples of thinking objectively about intuitive design decisions.
It'll be up to you to use those examples and apply the same thinking to other aspects of graphic design.
The Science Behind your Skill as a Designer
Deep graphic design questions like this are often dismissed as subjective, but this isn't true!
Just like science determines how the mind works, there is a science to graphic design. We artists, instead of using numbers and formulas, study the science of understanding and predicting the viewer's visual and mental interaction with (and response to) design.
Objective Explanation and Understanding of Graphic Design
Here are the points to focus on in order to bring your intuitive design choices and skills into an objective perspective so that you can understand and explain them beyond the scope of "I used this shape because it felt right."
- Focal Point(s): Graphic design of every medium, form, style, and purpose revolves around the design's success at drawing the viewer's eye and mind to the right place(s).
A well written explanation of focal point.
A quick summary:
Whether this is achieved by color, focus, positioning, or a combination of the three, the concept is the same: There are one or more specific areas on any logo, interface, ad, or page that you want the viewer to notice before he looks away.
For example, in this answer, I have designed the content to present your vision with grouped, organized information (points of focus) at first glance, rather than using plain, spaced paragraphs, which would likely leave your eyes scanning the text in boredom.
In the same way that you "intuitively" use a specific font, or icon, or section, or line width in an area of your design, I'm using spacing and font weight/size to present your eyes with a balanced set of visual content that you will feel comfortable with interpreting as I want you to, rather than skimming past it.
This is a low-level demonstration of the science involved in drawing the viewer's eye and mind to the content in the way that you, as the artist, intend.
You take in the spacing, balance, and focus that you see in your design and modify it until you predict that the viewer will see your design in the way that you intend.
- Design Emotion: The intent of stimulating the user's emotion through mood portrayal.
An enlightening article on the usage of emotion in design.
A quick summary:
Whether you're designing an anime character, or simply using an abstract shadow effect on an icon, as an artist, you work to affect the viewer's mind so that he feels a specific way after looking at (or interacting with) the design.
By using vivid (or gray-scale) color scheme, or portraying character activities, you attempt to cause the viewer to feel a specific emotion.
By designing a document, poster, or answer to a Graphic Design question with the proper measure of visual detail, you attempt to cause the viewer to feel visually satisfied while interpreting the information that you want him/her to absorb.
Finally, by combining this visual content with a specific color scheme and character or interface activity, you attempt to make the viewer to feel specific, complex emotions, while remaining visually satisfied, possibly for the duration of time that you want him/her to spend looking at a poster or ad (or TV show).
- Subject Matter: The importance of using the right subject to place the viewer's attention in the right place.
An in-depth lesson on the importance of subject matter focus.
A quick summary:
We can predict how a specific user group will react to a specific style, how he will feel about a specific activity, and where his attention will be drawn throughout the process, but it all acts as a modification to the core of the design: the subject matter.
As a designer, you choose the subject matter that you predict will cause the viewer to focus on the subject that you intend.
If the subject is the words and logo on an ad, you might use a single-color box with text as the subject matter for your design. If you want the viewer to be moved, you may use a touching image, or simply moving words.
Your intended effect on the viewer is centered on the subject matter that you choose for the design.
The Objective Summary
In the end, every decision that you make in the design of anything can be objectively observed and explained by looking at two things:
- How do I want my target audience to feel and react to the design?
- What do I predict as an artist, is the best way to achieve that feeling and reaction?
When you combine these two questions with the aspects of design explained above, you're able to objectively understand and improve your skill as an artist.
You wanted to know how you can understand the intuitive design decisions that you make so that you can explain them and also improve them.
That's a very good goal, and I think just by asking this question, you're already moving in the right direction.
By focusing on focal point, mood, and subject matter, you can understand and explain the purpose for each aspect of your design choices.
These are just a few of the many important areas of design, but by recognizing these, you'll be on your way to having a better understanding of why you make the intuitive choices that you do in Graphic Design,
Improvement comes through practicing your ability to predict a user's reaction to a specific design, and most importantly, your ability as an artist to put that design down on a medium just as you imagined it.
See the cited sources for a fuller understanding of these aspects of your intuitive design decisions if you have the time. If not, this should at least allow you to begin reflecting on some aspects of your design decisions in a way that you can learn from and explain them.