Every piece of writing has the potential to be read by others, but sometimes, other people are not your intended audience. For example, an outline for an essay has the intended audience of you, unless your professor demands to see the outline as part of the grading process for the course, and then, suddenly, it has the intended audience of the professor. A grocery list might be intended for you, or might be intended for a spouse or roommate.
We change the way we write when the intended audience is someone besides the author. And we change the way we write based on who the intended audience is. Let's say you're a rocket scientist. If you're writing a paper on rocket science for a bunch of rocket scientists, there's going to be a certain amount of shared experience that you assume your fellow rocket scientists have. If you're writing a paper on rocket science for a high school career symposium, you are going to assume that the high schoolers who want to learn about rocket science as a potential career don't have that shared experience. But they do have some shared experience: probably a basic grounding in introductory physics and math, and some ideas about what a rocket is.
So we tailor our writing to our intended audience.
When you're writing something that is personally important to you, be it in an essay format or as narrative prose, it's important to gauge the shared experience that you have with your readers. This can be true in fiction as well as non-fiction. For example, let's say you're still a rocket scientist. You want to write a suspense thriller that has to do with the rocket science industry. Think John Grisham, but with rocket science instead of law. If you write it with a lot of technical rocket sciencey jargon, it might be very appealing to other rocket scientists, but you've chosen to limit your readers to a niche audience.
This isn't necessarily a bad choice, but it's a choice. Some people only want to write for a very specific, limited audience, and that is cool, but some people want to write for the most generalized audience possible.
And sometimes you can't choose your audience. Which means that you end up with a different choice:
--Do you write for the part of the audience that will enjoy the exact same thing you do, and risk alienating the rest of your audience?
--Or do you try to find something that will appeal to the largest proportion of that audience possible?
Neither of these is a "better" choice, per say. But they do have different results. The former doesn't take a lot of extra effort on the part of you as a writer: you just keep on writing what you like to write. If you're really lucky, what you like to write is something that is really poopular with that very eclectic audience. If you're less lucky, what you like to write is very popular with a sliver of that eclectic audience, and they love you, but everyone else sort of says, "meh." And you live with that choice, to cater to a very selective audience.
The latter is a bit harder to do unless you're that very lucky person who really enjoys writing things that really appeal to a big group. You can still write what you like. But you need to walk a careful line between alienating your audience by assuming they are too much like you, and alienating your audience by assuming they are too different from you.
In the first case, you might write about rocket science, but forget that your audience doesn't know a lot of technical jargon or inside rocket scientist jokes. So people might get a sense of what you're trying to do, but not really quite get everything-- or they might think they're getting everything when in fact the jokes are going over their heads. If your rocket science jokes are too specific, even really smart readers might not realize you were making jokes. And this isn't just true with jokes; it can be true with a persuasive argument or even a piece of personal narrative.
In the second case, you might go out of your way to explain ideas or define words that your audience would be smart enough to figure out from context. It's a classic case of telling instead of showing. Say you use a very difficult word: do you define it? Most people will recognize that it is a difficult word that they don't recognize, and are capable of looking it up if they want to know what it means and don't understand it from context. Defining it can break the pace of your story, and can also make people wonder if you think they're not clever enough as readers.
I tend to be of the belief that most people are just as smart as me, but not necessarily as knowledgeable as me if I'm talking about a very specific subject in which I have a certain amount of mastery. This is generally a good rule to follow. Some people will be as knowledgeable as you, but not all. Most will be as smart as you, and many will be smarter than you. It's always important to have respect for your readers and to genuinely believe that they are as smart as you are, if not smarter. Everyone likes to be respected, and people can tell from your writing if you don't respect them, or if you're talking down to them, or if you assume that you're smarter than they are.
But it's also important to remember that specialized subjects aren't all things as intimidating as rocket science. They can be thinks like sports, television shows, or even the town where you live. You might take for granted that everyone knows what your regional grocery store chain is, because they have them in all the towns near you. But people in a different state or country won't know what you mean when you talk about them, unless it's obvious from context that you're talking about a grocery store. Even though many people have read Harry Potter, if you're a serious fan who has read all the books six times apiece and spends hours talking about theories relating to the books, you might make assumptions that everyone knows specific details of the books, whereas even someone who has read all the books once might be lost and confused when you start talking about a favorite pet theory that is so popular in Harry Potter fandom that you can take for granted when talking in fandom circles that everyone knows what you're referencing.
When you're writing about a very specialized subject, here are some questions you can ask yourself:
--How likely is it that my readers will understand my references in this passage?
Sometimes it is very likely-- for example, if you are talking about something really universal, they are likely to understand it. If you're talking about something that has to do with a specialized interest, it is a lot less likely. The more eccentric the interest is, and the more embedded in that interest the reference is, the less likely it becomes. For example, if you're writing about American football, you can assume that many people will know that a touchdown is a way of scoring. Slightly fewer people will know that a touchdown happens when the ball is run to or caught in the end zone, or that a touchdown consists of six points plus one or two possible extra points. Many fewer people might know the specifics of a certain player's touchdown reception statistics.
--Do my readers need to know what this means to understand what I am trying to communicate in this passage?
This is pretty self-explanatory!
--Will my readers who don't know what this means realize that they are missing something?
This is really important! If your readers realize there's something they don't get, they may go look it up on their own if it interests them. If they don't realize that they're not getting something (and are thus missing out on your clever joke or brilliant turn of phrase), then everyone-- you and your readers-- might be losing out.
--Is it necessary to the piece I am writing to include this information that readers may not be familiar with?
Sometimes, there's just no way of writing what you want to write without that specialized information. Sometimes, you might not actually need it at all. Think hard about whether it really needs to be there.
--Is there a way to make it clear from context what this thing my readers might not be familiar with is?
It's always better to avoid blatant exposition. Maybe you can work it into the story: if, in your story, someone scores a two point conversion, you might be able to get away without explaining what a two point conversion is. If someone in your story mentions in their dialogue that such and such player had such and such record, you might be able to make it sound natural and not like you are lecturing your readers.
If you can't figure out a way to get the information in without lecturing your readers, go back up to that question about whether it's necessary to include the information again. Because if there's one thing that can alienate a reader faster than not getting what something is about, it's making them feel like you think they're stupid.
Sometimes, lecturing is okay. If you're writing an informational essay, lecturing can even be good. You can get away with imparting information in an expository way, and people will enjoy it. But when it's inserted into another format, it can be really frustrating!
This can be a good place to get a beta reader. Give them a version of your piece without an explanation of the information that might be too specialized. Have them tell you if they felt it was clear to follow and double check any passages where you might be concerned that they may not realize that they're not getting something. They might get everything, and then you'll know that you're on the right track. If they don't get everything, that's a good time to try to insert more information, or cut references to specialized information that aren't necessary to understanding the story.
It's hard to find the line between leaving your readers in the dark and lecturing them, but when you do, you'll be able to write successfully about specialized subjects.