Rhetoric in Civic Life opens its first chapter with a paragraph meant to justify caring about symbols:
Human beings make sense of their interactions with the world and with each other through the symbols (the words and images) they attach to their experiences. Words (language) and images (icons, pictures, photos, bodies, architectural structures) are not merely a means to transmit information, they are the grounds for judgments people make about things, events, and other people. Quite simply, symbols matter.
Heavily condensed: Humans think using symbols. Put another way: Humans attach symbols to things in order to think about them. When I think “rock,” I don't conjure up a literal rock in my mind. If that were true, everyone that ever watched a Michael Bay film would have had their heads explode. (Well, really, we'd all be dead before breakfast – caffeine shouldn't be injected directly into the brain.) No, when I think “rock,” I picture in my mind a symbolic rock. If I think of a small rock or a brown rock, I modify my standard mental image of a rock enough to fit. If I want to think more precise thoughts than just “rock,” I need more precise symbols. In order to think about anything at all, one must have a symbol to represent it. Can you imagine thinking about something you can't imagine? The thought itself feels like an oxymoron.
Being able to think about the external world isn't a strictly human trait. Dogs have brains. Insects have nervous systems. There was one MythBusters episode where they tried to prove that plants have feelings. Sentience (as far as we know) is what sets man apart from beast and (among other things) plant. Humans don't just think; humans think that they think. A shocking Google search revealed there already exists a symbol for just this thought: metathought. If symbols are the building blocks of thought, having a symbol for thought about thought is actually thought about thought about thought, which is just the beginning of a very long train of thought concluding (kinda-sorta) in meta-to-the-nth-power-as-n-approaches-infinity-thought; a meta-train, for short, with reality at the bottom, thought just above, meta-thought just above that, and a whole lot of other stuff that makes little sense above and below it.
Metathought is worth thinking about. Metasymbols (a symbol I did get to make up! Eat your heart out, wiktionary!) are necessary for people to be aware and make sense of their existence. For instance, “I” is a metasymbol, as are most of the words that can follow it (i.e. “I think I have writer's block”), but this isn't meant to become an English lecture. Symbols are tools, and tools shouldn't be forged or even picked up without a purpose.
Symbols allow us to think about what they represent. Thinking is good. Thinking gave humanity lots of cool stuff, like agriculture and the entirety of civilization and just about everything else that can be attributed to the species. Being able to think about thought enables us to think better. Refining our metathought-vocabulary (another symbol that's all mine... probably... not gonna risk another disappointment like finding “metathought” on wiktionary...) allows us to think more precisely about thought, like small thought or brown thought. To repeat my title, a phrase from a future citation, “Understanding your understanding” is important to improving thinking and, consequently, everything below it in the meta-train.
LessWrong is a “community blog devoted to refining the art of human rationality.” It's a very STEM-focused community, with a lot of its funding and leadership coming from institutes seeking to bring about the “AI Singularity” (and which hates to discuss Roko's Basilisk – not my fault if you Google it an develop a new fear). The community produces quite a few useful tools in their quest for rationality, but they're rather cumbersome for the uninitiated to pick up; the community maintains exceptionally self-referencing, jargon-laden communication standards. LessWrong is, at its heart, a bunch of CS majors trying to rewrite and rethink philosophy and psychology in their own terms.
That's not to say it isn't useful. This post serves the same purpose mine does (and lends its title), just in a way that is entirely unfriendly to the uninitiated. It needs remixed for a broader audience.
Understanding your understanding:
Level 0: Aware, but not understanding
You have big, fancy words in your vocabulary that mean nothing to you. If you're a talented rhetorician, you can probably feign understanding simply by spewing enough jargon, but you don't really know anything. Your fancy vocabulary is a collection of symbols all understood to be related, but not related to any real world concepts. You cannot use them to think about the world around you.
Level 1: Isolated understanding
Your vocabulary corresponds to the real world, but in a very specific way that doesn't really make sense. The epitome of this level of understanding is high school physics class. You have all of these formulas, you know they all work, and you know how to use them, but you don't know how they work or why they work. You can use your understanding to help you think about the real world, but you aren't entirely sure which formula to use when, and sometimes you make surprising mistakes.
Level 2: Connected understanding
Your vocabulary makes sense within your broad picture of the world. Instead of each individual formula fitting a specific event because your teacher said so, each formula fits a specific event because your real world experiences indicate that it does. Your understanding can not only be usefully implemented, but accurately applied to predict future events.
Level 3: Regenerative understanding
The symbols in your vocabulary are well defined and heavily correlated with your understanding of the world. If you were to forget some of the symbols, you would be able to re-derive them for the same reasons you understood them before. You understand the world around you so well that the symbols you possess are redundant. You can recognize what was lost because you still have it, filed away under another symbol from a related domain of thought. You can implement your understanding usefully, accurately apply it, and reconstruct it for yourself.
To give examples: We all have a level three understanding of addition, hopefully a level two understanding of rhetoric by now, (for those of you in chem with me) a level one understanding of chemistry, and (probably – we should be friends if this doesn't apply to you) a level zero understanding of quantum mechanics.
Having symbols that precisely define our understanding allows us to think and communicate precisely about our understanding. We can recognize when disputes arise from deficits in knowledge, or when they arise from using different symbols for different concepts. This spares us the embarrassing rhetorical situation of debating definitions and allows us to focus on more important matters, like desperately studying for finals.