Perspective is an existential fundamental, meaning that it's an archaic concept relevant to every layer of the artistic experience. The "perspective" we use and talk about in art is the same perspective or POV that we talk about in writing, philosophy, and all other disciplines.
Some aspects of it have a geometric component unique to visual art, which we will discuss, but not all of them do.
I don't want to get into all the things perspective is not, but I do need to acknowledge that perspective is a widely misunderstood and misrepresented topic in art.
So if you've heard things like "perspective is shading that adds depth" or "perspective is drawing things with more than one side" or "perspective is anytime you rotate objects," just be aware that these are incorrect by this platform's standards and set them aside in your mind for now.
Instead, let's look at what perspective is.
Perspective means to have a limited "view" of something due to the "point" in space (i.e. the position) one is or has occupied. Hence why it's also called "point-of-view" (POV). The two terms are synonyms.
As mere mortals, this is how we fundamentally experience the world. We are not omniscient to everything happening everywhere. We can only get a distorted glimpse of the environment that immediately surrounds us when it is sufficientely lit. We can only hear the soundwaves that manage to traverse to our very particular location in space.
And even then, how we interpret those sights and sounds and other sensory cues is heavily dependent on what we have previously experienced, our knowledge, and our perception of the environment.
Consider the difference between hearing rapid explosions while walking through an unfamiliar city at night and fearing them to be gunshots, versus hearing that sound at a local fireworks display and understanding them to be part of the show. The sound may be similar, but our perception of it changes due to the context of our perspective.
That doesn't mean our perception is more accurate merely because we have context and experience informing it. There may very well be a gunman at the show, just as there may very well just be some jolly folks setting off fireworks in the city. But our brain selected what it decided was the most likely given our current and prior perspective, enabling us to make a more informed decision regarding the next action we take.
It is physically impossible for a human being to experience the world objectively. Everything we think and do and perceive is all happening through our subjective perspective. Both what we are immediately experiencing and the sum total of our prior experiences, long embedded into our memory.
While there are no limits to how this applies to visual art, I do find it helpful to break perspective down into a few different categories:
Optical Perspective pertains to the visual geometry of seeing a space from one position in space and how we can capture that in art. One reason we use this technique is that images drawn in perspective are more familiar and easier to understand, because humans are used to seeing the real world in perspective througuh their own eyeballs. Whereas an orthographic drawing -- like a floorplan or isometric view, which illustrates something from an angle rather than a POV -- is very difficult for the human brain to parse at a glance. Even when it communicates the exact same information, the average viewer can't fully digest it.
Tonal Perspective pertains to the implied thoughts and opinions of the perspective character, who is often presumed to be the artist themselves. In writing, the way your narrator talks about a character, object, or idea in contrast to others communicates how supportive or disdainful they are towards them, even when that was not the writer's intention. Likewise, how you render or otherwise present something has the same effect in visual art. The tone you choose to draw with affects the viewer's impression of the work, its subjects, and you. This isn't a perfect science, and the viewer's own media literacy plays a big role in how well equipped they are to process and understand this aspect of perspective.
Narrative Perspective pertains to the perspective of the subjects or characters, whether they are depicted or implied. How are we communicating their circumstances? How are we transitioning between their points-of-view? While tonal perspective revolves more around judgement, narrative perspective revolves more around empathy (https://lib.hol.ink/index.php?topic=24.0) and how we see through those characters' eyes in their own world. Consider the scenario where we have our main character fighting a grand beast. Are they fearful or confident? Are there obstacles they or the beast could hide behind? Can they tell there's another enemy trying to ambush them from where they are? Are they distracted checking in on a fallen comrade? Can the comrade see the ambush, and are they trying to communicate it? These narrative issues are fairly conceptual, and we might not literally see optically through each characters' eyes in each frame. (Even in a comic, that kind of direct POV switching can be difficult to pull off.) But we could still recognize and experience all these perspectives, even in just one well-arranged image.
Compositional Perspective pertains to the eye movements, impressions, and emotions of the actual human being looking at the art. The viewer's eye settles on focal points in anything they are looking at, including our art. These focal points are typically small areas of contrast, with different types of contrast holding different positions in the hierarchy of attention. From the eye's center-of-view, there's a gradient where less and less information types can be identified further from the center it gets. For example, text can only be identified in about the innermost 5 degrees of our vision. This in turn limits the types of contrast we can notice based on distance. These two ideas combined let us control the viewing order in a work of visual art. While other concepts let us influence first impressions, emotional responses, and such.
These categories make it a bit easier to communicate with students so they know which aspect of perspective is being discussed. I don't want to be critiquing the perspective implied by how something is rendered and have someone think I'm saying their camera is in the wrong spot, you know? We can end up talking in circles.