I don't know if you are aware that this is documented in details.

The problem is that the informations are dispatched over the documentation of PDECoefficentData and InitializePDECoefficients.

your code :

{state} = 
  NDSolve`ProcessEquations[
   With[{u = u[x, y]}, {-2 D[u, y] - 3 D[u, x] == 1, 
     DirichletCondition[u == 0, True]}], u, {x, 0, 1}, {y, 0, 1}];

data = state["FiniteElementData"]["PDECoefficientData"];

data["All"]
(*{{{{1}},{{{{0},{0}}}}},{{{{{3,0},{0,2}}}},{{{{0},{0}}}},{{{{0,0}}}},\
{{0}}},{{{0}}},{{{0}}}}*)  

The PDECoefficentData documentation explains this :

data["ConvectionCoefficients"]
data["DampingCoefficients"]
data["MassCoefficients"]
data["LoadCoefficients"]
(* etc ... *) 

{{{{-3, -2}}}}  {{0}}  {{0}}  {{1}}

InitializePDECoefficients documentation :

The DampingCoefficients and MassCoefficients are explained beyond.

I don't know if you are aware that this is documented in details.

The problem is that the informations are dispatched over the documentation of PDECoefficentData and InitializePDECoefficients.

your code :

{state} = 
  NDSolve`ProcessEquations[
   With[{u = u[x, y]}, {-2 D[u, y, y] - 3 D[u, x, x] == 1, 
     DirichletCondition[u == 0, True]}], u, {x, 0, 1}, {y, 0, 1}];

data = state["FiniteElementData"]["PDECoefficientData"];

data["All"]
(*{{{{1}},{{{{0},{0}}}}},{{{{{3,0},{0,2}}}},{{{{0},{0}}}},{{{{0,0}}}},\
{{0}}},{{{0}}},{{{0}}}}*)  

The PDECoefficentData documentation explains this :

data["ConvectionCoefficients"]
data["DampingCoefficients"]
data["MassCoefficients"]
data["LoadCoefficients"]
(* etc ... *) 

{{{{0, 0}}}} 

{{0}} 

{{0}} 

{{1}}

InitializePDECoefficients documentation :

The DampingCoefficients and MassCoefficients are explained beyond.