According to the first answer in this post, a conormal distribution $u$ on a manifold $X$ relative to a (closed, embedded) submanifold $Y$ is an element of a Banach (or Hilbert) space $H$ such that for any positive integer $k$, we have $$ V_1\cdots V_k u \in H $$ where $V_i$ denotes a vector field that is tangent to $Y$ (smooth and unconstrained away from $Y$).
I would like to better understand these objects. Hence I was wondering whether somebody could suggest a good example for a conormal distribution, or more detailed explanation of what these distributions "look like" ?