In chapter 22 of how to brew by john palmer there is a section called adjusting water for style. further down there is a handy brew cube:
Across the bottom there is a vector called "beer structure" with measures of soft, medium and firm - this is based off the calcium in the water.
there are no references to beer structure anywhere else in the book and everywhere else on the internet - it's like it's just been made up for the book.
What does it mean/feel/look/taste like?
In this case, structure refers to the perception of mouthfeel.
My guess is that he is referring tangentially to mouthfeel, I have never heard of beer structure as a vector of beer quality.
Let Me Google "Beer Structure"... not really anything there (12 Jan 2018), I feel he may have just made up a term, which being John Palmer I think he is entitled to do.
I had a Talk with Palmer, and Beer Structure it's the Mineral Structure, how much Minerals the Water on the beer has.
The total Dissolved Solids, he says all the beers are soft and medium. He says he only knows a Firm or High Mineral Structure Beer, and that's Dortumunder Export, it's a light beer but it doesn't taste like that because its water it's really high in the amount of Minerals.
He answers it here it's about 16 minutes in, and at about 29 minutes in https://youtu.be/bKKPxXUg15Q
I've only seen this term in reference to wines and how tannins give "structure".
If I had to guess I would say this is how the bitterness from IBU is perceived in the beer. For example doing a FWH will have a "softer" bitter perception than a normal bittering addition of the same IBU.
Though "firm", "medium", "soft" are usually descriptors for mouthfeel and head texture.
