What exactly is controled for in a model with country, industry, and year fixed effects? I don't have much experience with panel data so I apologize in advance if this sounds ridiculous.
I am currently writing a thesis investigating the impact of political risk on managerial risk-taking.
I control for various variables that are known to affect managerial risk-taking and include dummy variables for industry, country, and year (these are the fixed effects).
What exact unobserved variables are controlled for in a model with multiple fixed effects?
My understanding is that the coefficient estimates show the average effect the explanatory variable has on the dependent variable across groups. How are those groups exactly defined, when industry, country, and year fixed effects are included?
Would the group be industry-country-year such as retail-UK-2019?
 A: Your interpretation goes in the right direction, but it does not sound fully correct to me.
It's important to interpret any coefficient for political risk as a conditional estimate: It compares managerial risk-taking between different political risks given a certain level of all other covariables. In your case, this means in a given industry in a given year in a given country. So you are essentially comparing within a country, industry and year (that's why it is also called the within estimator). So note that you are not comparing across these "groups", but you are holding them constant.
Note that your dummies only allow to estimate one effect for each year, industry and country, but not for each combination thereof (which would requrire interaction terms - which are probably not an option given the degrees of freedom they soak up).
As an example, your fixed intercept for the year 2012 will apply to all observations, those from Kenya and those from Fiji. If you would like to know the average managerial risk-taking in the group "retail-UK-2019", given your model and covariables, you'd have to sum up the intercepts for "retail", "UK" and "2019".
For more on this, see also this great beginner econometrics resource.
