Congruent matrix

Two symmetric matrices $A$ and $B$ are defined to be congruent if there exists an $S$ in $GL(n)$ such that:

From effect of a change of basis on the matrix of a bilinear form, remember that a change of basis $C$ modifies the matrix representation of a bilinear form as:

So, by taking $S=C^T$, we understand that two matrices being congruent means that they can both correspond to the same bilinear form in different bases.