Fovea is relevant in case of forms and resolving proximity issues for example.
If you put error messages too far away from the cause of the error (like, the field which was left out), people aren't able to make a connection.
However, if there are other red elements as well, they aren't able to make a connection either.
This is a screenshot from Jeff Johnson's wonderful Designing with the Mind in Mind
(Chapter 8 is about Peripherial vision)
How you should think about it?
Your mind works the following way: your eyes can see only clearly an area which roughly equals to your thumb with your arms stretched in front of you. The rest is behind a fog basically.
But your eyes can move rapidly and your brain can act as if it remembers.
So, whenever you enter a new space, or a new screen appears, you quickly scan it, in a few seconds. From that on your mind works "from cache", that is, it has a visual memory (and sometimes, an artifically constructed image) of how things should look like around, and you see the only thing you're directly looking at.
I guess - albeit I'm not expert - this can play a role on why most people fail on the gorilla test.
How does it affect every day UX practice?
It comes out usually on usability testings, when people can't see things despite being "in front of their nose". That's partly because of the fovea.
It also comes out with eye tracking tests: these are so-called gaze plots.
As eye tracking normally watches your eye with an infrared cam, such shows where your fovea points at. The sizes are however not necessarily connected to a scanning.
Is it only the fovea which is relevant?
Not at all! In her wonderful book, 100 Things Every Designer Needs to Know About People, Weinschenk refers to the Larson-Loschky experiments, which tell us that peripherial vision is more useful to make us know what to look at.