The best way to explain anything to a non-expert is through giving examples. So the best way to explain what Emacs is is all about to a civilian is to give examples of use cases they can understand and relate to.
I usually start by saying something like this: Emacs is an old-school text-editor from the 70s that was invented before Microsoft Word and all the modern word-processing apps. The reason it's so cool is that it's programmable. It has a programming environment built into it, which means you can write and edit with it the same way you would with Microsoft Word.
But since Emacs is programmable, you can literally program it to do anything. And since it's programmable, you can integrate Emacs with anything else on your computer, including your browser, your email, your contacts, your calendar, Twitter, Evernote, and any other programming languages you use.
Everyone who uses Emacs programs it to do different things based on what they need. So a web developer who uses Emacs might program it to do __ and __. A scientist or academic might program it to do statistical analyses with R and...
In my case, since I'm a writer, I've programmed Emacs to do things that help me with research, writing, and editing, including:
- when I'm doing research and I copy and paste text from the web, automatically format it as a block quote, and automatically copy the name of the page, the URL, and the date and create a bibliography entry
- search and replace text phrases across multiple files in a directory
- when I write something, to automatically export to a nicely formatted web page, and, from the same source document, automatically export it to a nicely formatted PDF file, automatically generating a cover page and table of contents
- help me keep track of my todo lists, appointments, and deadlines
- help me brainstorm ideas and create mind maps
- automatically send emails to people, and automate certain kinds of email replies
I generally conclude by saying something like: Basically if there's anything you do on a regular basis as part of your workflow, Emacs can be programmed to do it automatically. So basically it's a tool for programming your text editor to do whatever you want.