Reddit reviews The Symphony: A Listener's Guide

Hi Owen. What you're looking for is very specific to each piece. But I think a good place to start would be in collections of program notes. Program notes usually have a little bit of history about the composer, a little bit of history about the piece, and if there's a story then they usually include a short synopsis.

So you can often find something close to what you're looking for by just searching for the name of the piece and "program notes." Lots of orchestras put theirs online.

Or if you're interested in some good books, I recommend Michael Steinberg's two collections of program notes,
The Symphony
and
The Concerto

If you happen to have access to the JSTOR online database, I think you'll find it to be the best place to take a deep dive into more detailed analysis.

EDIT -- I'll add that sometimes wikipedia can be a decent resource. But I regularly find major errors in the analysis of various pieces. I often get the feeling that some of the wikipedia entries for orchestral pieces come from class projects where students are instructed to find a piece that doesn't have a wikipedia article about it, and to create one. But the advice I gave to my graduate students was always "go to wikipedia first -- if you see references at the bottom of the wiki entry, go check out those references. They're probably better than the wiki article."