The answer in this post describes the solution to this linear system
$$ \begin{aligned} Ax &= b \\ L L^{T} x &= b \end{aligned} $$
as solving the two triangular systems.
$$ \left \{ \begin{aligned} Ly &= b \\ L^{T} x &= y \end{aligned} \right. $$
I use this solution often and was recently asked, "what is $y$?" I commonly brush this off as being just a vector serving the provisional values for step 1, but are not of substantive interest. What we really want is the solution to $x$.
My statement is true-ish, but lacks a mathematically rigorous answer for "what is $y$?"
What might be a more sophisticated and rigorous answer for explaining what $y$ is in this solution?