In the early pages, there's a brief summary taking up about a quarter of the page.
Later, A 1-3 page article. Often the issue will contain multiple papers on the same subject, this article is a simple-english aggregation of those subjects.
The research papers themselves are published later on.
For example, Nature published two recent papers on the determination of the Thorium nucleus's excited state. The papers themselves would have meant very little without a physics degree or some serious determination, but the accompanying article explains all aspects of the papers well. It explains the context (why are these papers significant), how the two papers relate to each other and the broader implications.
Having read the article, it's then much easier to comprehend the contents of the paper. Not easy, but easier.
Nature's not cheap (£198 a year), and it comes weekly which may be faster than most people can read it, but as a means of communicating the absolute cutting edge of all sciences I commend it.
You're saying that a bit under £4 a week isn't cheap? As a child my parents bought National Geographic monthly, which wasn't cheap where we lived, but it was well worth it. It threw me face fisrt into a lot of scientific knowledge and amazing photography which I wouldn't have accessed through any other means. I wouldn't call £4 a week expensive.
A paper is not source code - it is a tool for scientists to share their discoveries with fellow humans, and fellow humans will always appreciate clearly expressed ideas. After all, what good is a tool for knowledge sharing that's accessible only to a few? Now, I've argued before that some papers are necessarily difficult (because the topic is very specialized) and I stand by it. At the same time I do think a good paper should attempt to reach as wider an audience as possible, and jargon goes against this concept. I think the joke that "Git gets easier once you get the basic idea that branches are homeomorphic endofunctors mapping submanifolds of a Hilbert space" illustrates this concept beautifully.
For non-toy examples, there are notes freely available on Donald Knuth's "Mathematical Writing" course [1]. These notes are a must read for scientist, and they include several examples of how replacing jargon with plain English can do wonders to improve readability. Page 7, in particular, explains how to rewrite a proof that "is mathematically correct (except for a minor slip) but stylistically atrocious".
[1] http://jmlr.csail.mit.edu/reviewing-papers/knuth_mathematica...
To borrow your joke, please transform "homeomorphic endofunctors mapping submanifolds of a Hilbert space" into plain language with no loss of precision.
On one hand, writing that into plain language would take forever. By the time I'm done, I would have probably written a small book on algebra. Here, the use of jargon is definitely precise. If you wanted to present this in a topology conference, where it might be important that the number of dimensions of the space is infinite, it would be probably a good start.
On the other hand, thousands of people use git everyday without understanding a single word of this description. But if I say instead "git is a distributed version-control system for tracking changes in source code during software development", my clarity has now skyrocketed. I definitely lost a lot of precision, but my readers will still be able to replicate my results.
That's not to say that there is no necessary jargon - my own definition uses "distributed version-control", which is absolutely key for understanding what's going on.
I've had this sort of trouble also. The way I was taught to resolve it was to define every bit of jargon you use, or at the very least refer to some previous work's definition of that term - _and then stick to that definition come what may_.
So if you use a term, even if you want to use it in a somewhat uncommon manner, define it, and if possible define it before using it. It's like coding, right? Er. In C, anyway, if memory serves.
As other commenters have noted, plain english is imprecise. When communicating with other scientists in the field it is often necessary to use language that conveys an exact meaning within their pre-existing body of knowledge.
If the audience is people without this knowledge, the precise meanings are useless and can be ignored and rigorous quantifcations are often unimportant. However, this is frustrating to scientists who are then left wondering which of n different definitions of some property/parameter you are using and how this influences results. This is critical knowledge when internalizing and applying new information.
I am also adding in many "over-elaborations" because the reviewer had questions that a simple adjective or two would have answered. A paper absolutely ~is~ a dialog with potential questions, and nothing illustrates this more than peer review.
The two audiences require different papers, and peer reviewers tend to fall only into one of them.