In any area of expertise, a fundamental is a core, foundational theory from which more complex topics are derived. Everything else is based upon and dependent on these ideas. While any path of study will eventually lead one back to the fundamentals, it helps students if they are covered early and classes "scaffold" up to higher-level topics.
When it comes to hands-on technical skills, a key milestone in one's studies is achieving automaticity with each level of its fundamentals. Meaning that the goal with a fundamental is not just to achieve conscious mastery (a logical understanding of the theory) but to achieve unconscious mastery (a deep familiarity that no longer requires logical thought). This allows you to pursue more complex ideas that use that fundamental skill in peace. If you don't reach this milestone, it's deeply exhausting to apply the things you're learning in practice, and even simple tasks can lead to burnout.
Aside: Although many art classes try to skip it in the guise of "pure intuitive training," true automaticity generally cannot be achieved without first achieving mastery over the theory. That mastery gives your brain the formula it needs to skip the hard parts later. Automaticity is also best trained at each minor stage to minimize overwhelm. If you imagine yourself reading a textbook about, say, lighting skills, then automatic training should begin after each sentence or paragraph is digested, NOT after entire chapters or volumes pass by. But we'll talk about this more elsewhere.
In art, we can understand the fundamentals to be the underlying theories that apply to even the simplest of subjects, to works with no subject at all, and to the overall experience of learning and creativity. (A subject is the "thing" you are drawing, painting, etc. Abstract art lacks this.)
For example, if I described how a camera was looking at a particular arrangement of children's building blocks with words, someone who understands and has practiced the fundamentals of constructive drawing sufficiently could position everything accurately in space and render it photorealistically with only the given information. And they could do so quickly and confidently with little thought.
When we jump right into learning how to draw flashy things like 3D comic book characters and intricate environments, the complexities of everything else involved in depicting them overwhelms us and obscures the basics. We become preoccupied with these more niche, higher-level topics, like human anatomy or architecture, but then can't even use what we've learned because we have no foundations to apply them to.
Training these skills doesn't need to be boring, and if it's scaffolded properly, it shouldn't interfere with your ability to make complete works featuring things that interest you from the start. Learning the fundamentals doesn't mean you can't design characters or tell stories or do other fun things with your art. However, we may have to break those ideas down further and lower our expectations a bit in terms of the style and approaches we use early on.
Compared to other fields of expertise, art does not have much in the way of a standardized language.
This probably resulted from the way art was traditionally taught in a deep vertical manner as opposed to a broad horizontal one; you would be part of a particular artistic lineage with concepts, terms, and ideas that were only passed down to other disciples of your master or school.
With our increasingly global society and internet access, these ideas have been blending together, which is wonderful. But it also makes it extremely confusing for beginners. Even experienced artists can end up talking past or arguing with each other because they're using the same words in different ways.
So if I just start rattling off a list of the fundamentals without context, it won't actually mean anything. Something like "perspective" or "value" could refer to dozens if not hundreds of different topics and skills. And only some of those will be relevant to where you are at on your own journey.
So instead, I will make an effort here to distinguish the different groups and forms these ideas can take. This will then be referred back to in later discussions to clarify what aspect of a fundamental we are talking about.
Existential Fundamentals
These fundamentals are integral to human experience at its most base level. They apply to everything in life and all forms of art -- visual, auditory, performance, or anything else.
You can think of the existential form of a fundamental being an umbrella term that encapsulates all aspects of it. It's not limited in scope.
For example, when we talk about existential perspective, this would include more philosophical ideas, like how your personal background (life experience) affects how and why you make your art.
Not all art fundamentals have an existential aspect, and not all skills with existential significance are considered fundamentals.
I also include skills that affect your experience with learning and creativity more broadly at this level. Like how you study might not be a proper art fundamental, but how memory works is an existential fundamental that will inform how you choose do so. Basically, some important skills branch off from here without touching the other categories below.
Disciplinary Fundamentals
These are fundamentals in the context of a particular artform. This site is more heavily centered around 2D visual art at the moment, and so that is usually the context. But I did want to mention this to be clear that a concept can share a name but mean something very different depending on whether we're discussing music, art, performance, and so forth.
Compositional Fundamentals
Within each artform, these fundamentals apply to the "surface level" of that form. Basically, how is that art experienced in its form by its consumer? How does it make them feel? What's the significance of its arrangement?
How exactly it was made is generally considered irrelevant at this level.
For example, in a theatre show, the 3D arrangement of sounds is part of these compositional fundamentals, but exactly how you connected the wires of the speakers to achieve that result may not be.
These fundamentals are generally split into two groups at the most basic level: Your "elements of art" and your "principles of design."
The elements are the pieces you have to work with -- your colors, instruments, shapes...
The principles are the relationships between those elements and their effects given how you chose to arrange them -- how they contrast or harmonize with one another, how they draw attention to themselves...
But more complicated fundamentals can also be thought to have compositional aspects to them, because they inevitably affect the final product.
Applied Fundamentals
These fundamentals have to do with the actual techniques and theories that are being applied when creating. What form these take and the significance of each varies depending on the approach you take to creating your art.
I spoke earlier about how you can still make interesting things early on when studying the fundamentals. This is made possible by studying fundamentals only within the scope of the approach you are currently learning, on top of being mindful of the order you learn the approaches in.
For example, if your current focus is on copying sight or individual photos (making portraits, still lifes, landscapes, etc.), you can start making cool things a lot faster if you don't spend too much time on optical perspective, because that element of perspective has already been solved for you by the camera or your own eyeballs. It's a different branch of the skill that isn't as fundamental to your current pursuit.