Imagine you have a long rod. It is of length $l$ and diameter $d$. The rod has a length axis of length $l$.

Transverse is splitting the rod in two along its length axis. We place the rod in front of us such that it is length $l$ from left to right. Then we slice the length in two.

Lateral is splitting the rod in two along its diameter axis. We place the rod in front of us such that we see a circle. Then we slice the circle in half.