What is congruence in lambda-calculus
Generally speaking, in algebra, a congruence relation is an equivalence relation such that operations on equivalent objects yield equivalent objects. In the lambda calculus, a congruence is an equivalence relation such that constructing terms from equivalent terms yields equivalent terms: if $M \equiv M'$ and $N \equiv N'$ then $M\,N \equiv M\,N'$, and if $M \equiv M'$ then $\lambda x.M \equiv \lambda x.M'$.
“Alpha congruence” is another name for alpha equivalence, which is the relation such that two terms are alpha-equivalent if they are, intuitively speaking, the same except for renaming internal variables. Since this is not only an equivalence but even a congruence, it's called both “alpha equivalence” and “alpha congruence”.