The first clue for readers outside of the software field lies in What does artifact mean? on Programmers SE. Quoting the accepted answer (emphasis mine):
In software development life cycle (SDLC), artifact usually refers to
"things" that are produced by people involved in the process. Examples
would be design documents, data models, workflow diagrams, test
matrices and plans, setup scripts, ... like an archaeological site,
any thing that is created could be an artifact.
Artifacts in this sense are not only "created things" but also informative things; consider them both the explicit and implicit documentation of a process. The key thing to realize is that these artifacts help their audience to understand something about the process that generated them—or more concretely, they explain some use of a tool, intent of a design, application of a concept, etc.
Like archaeological artifacts, our questions and answers can be searched for and found. Like archaeological artifacts, they may have been buried somewhere, albeit in the mind of an expert or the pages of an esoteric text rather than under a mountain of ash. In this metaphor, Stack Exchange is sort of like the Smithsonian Institution, with each community representing a museum or research center. The artifacts are the Q&A, divided among those communities and cataloged within them via tags.
While this usage may not have originated on Stack Exchange, it's one that Joel Spolsky and Jeff Atwood often turn to when talking about the network they founded. Here's Jeff's take on meta.discourse.org:
Stack Exchange is primarily designed to service search engines and
produce useful artifacts. For example, when searching for a
programming problem, Stack Overflow is one of the first hits (often
the first!); users click the link, read what people have to say, then
go back to work. Write once, read thousands or millions of times.
Like the artifact in a museum, the artifact on Stack Overflow was produced by a small number of individuals and consumed by a much greater number of individuals looking for some knowledge. In either situation, if the viewer is a professional in the applicable field, the knowledge they're seeking is useful and practical. Unlike the artifact in the museum, users here can interact with most (but not all) of the artifacts Stack Exchange collects, because instead of being clay pots or data models they are Q&A. Here's Joel's take in an answer to another MSE question:
This is a community-generated site. It works by getting lots of people
to make different sized contributions which, we hope, in the
aggregate, collectively produce an artifact that makes the Internet
Collectively generating useful artifacts is tricky. Wikipedia was one
of the first and most amazing examples of the phenomenon....
The artifact we're trying to generate here at Stack Overflow is
intended to be valuable to learners at all stages of their learning
process. As such you need honest questions about basic things and you
need amazing answers to those questions.
So the artifact is not just a question and not just an answer. If it were just a question, people wouldn't be able to use it; if it were just an answer, people wouldn't be able to find it.
A better, more thorough treatment of the "artifact" metaphor comes in Joel's presentation titled the Cultural Anthropology of Stack Exchange. This presentation exists on the internet in several forms; I'm going to quote from the transcript of this 2012 recording at Google. The most relevant bit starts with "We hate fun" at 27:55:
...there's a lot of things you could do in discussion groups online
that don't really leave a useful artifact behind on the internet. So a
very, very important observation, which I have to keep repeating again
and again and again, because nobody gets it. But this is the most
important thing. If somebody asks you about the design principles of
Stack Overflow, of Stack Exchange, the most important thing you have
to remember is that the question is asked by one person. It's answered
by, let's say, one to four, five people usually. But it's viewed by
hundreds of people. And hundreds of people will get benefit from that
question, out of just that one person who asked for it. So if you ask
us who we're optimizing for, it's not the person asking the question.
It's not the people answering the question, although we want them both
to be somewhat happy. We're doing this all for the hundreds of people.
A very fundamental part of the initial design direction of stack
overflow is that Google is the user interface to Stack Overflow.
You're on our site because you typed a question on Google. I used to
say search engines. [LAUGHTER] Google is our user interface. You typed
a question on Google, and you found a page. And if we have inventory
there, it has to be really good. And that means everything is
optimized for creating this great artifact, this historical record.
The full presentation is about 35 minutes followed by 20 minutes of discussion and I highly recommend viewing it in full, if you have the time. Joel comes back to the artifact metaphor a few minutes later while discussing a close reason that no longer exists at 32:54:
Once again, opinion, debate, argument, polling, extended discussion.
They're great things. But they do not create an artifact. They do not
create a useful resource that anybody can learn from.
This is the nutshell definition of the term on Stack Exchange—an "artifact" is simply a resource that people can learn from.
The implications of "useful" are many and varied, and it's the job of each community to define them on their Meta sites.