Categorical variable as explanatory variable (right hand side)

In a linear probability model, or any sort of regression, one can use fixed effect estimation by simply adding in a STATA code i.something. This “something” can be either a village, a county or a country. When doing so one look at variation within this geographical unit, as follow:

$Y_{ivt} = B_0 + B_1X_{it} + B_2X_{vt} + alpha_v + epsilon_{vit}$

Where indexes $_i$, $_v$ and $_t$ represent respectively individual, village and time dimensions. The term $a_v$ stands for village fixed effect thus any regression will look at within village variation.

STATA code (1) : reg Y Var1 Var2 i.village, vce(cluster village)

Here I come to the point. In the set of covariates that I am using there is one categorical variable taking several different values. This categorical variable can represent colors, insurance company or ethnicity etc. In STATA I introduce this variable as i.categorical. Thus the STATA code becomes:

STATA code (2) : reg Y Var1 Var2 i.categorical i.village, vce(cluster village)

I have a hard time interpreting the implication of this regression. When running such regression, am I looking at variation within categories within village? That is looking at variation in Y for individuals belonging to the same category within a same village.

Thank you!