Depth in Mathematics
In math, the distance between the nearest end and farthest end of an object is its depth.
For example, Jane measures a box. When she measures the distance between the end of the box closest to her and the end of the box farthest away, Jane measures the box's depth.
Depth in Liquids
For liquids, the distance between the top or surface of the liquid and the bottom of the liquid is the liquid's depth.
For example, water is a liquid. If you fill a container with water, the distance between the top of the water and the bottom of the container is the water's depth. If the depth is big we say the water is deep.