A trench in general results when you dig a hole in the ground which extends for some distance. Imagine you are on top of the grand canyon looking down. What you are seeing is a huge trench that is lower than the surrounding ground.
Now imagine that you are on the bottom of the ocean and the bottom is all flat. Then you would be at the deepest part of the ocean. Now imagine that you have a gigantic plow that can start digging into the bottom of the ocean floor. As you dig you will go lower and lower below the surface of the ocean. In other words you will be going deeper and deeper below the ocean's surface.