Why do trenches form at some plate boundaries?

The Earth is made up of a thin crust of cool hardened rock that floats on a huge ball of of molten to semi-molten rock. This crust is broken up into multiple large parts called tectonic plates. The molten rock underneath undergoes "convection", like a slow boil, that causes the plates to shift on the surface. This happens extremely slowly at a rate of about a few centimeters per year.

When these plates move away from each other, they create gaps or trenches. There are many notable examples of these trenches, for example, the Mariana Trench as well as the trenches that were so useful to the allied forces during the various world wars where they would take cover from enemy artillery.