Depth refers to a type of vertical distance, where vertical distance is the difference between two vertical positions. One of the most common everyday examples of depth is its use in reference to water. The depth of the water is the perpendicular vertical distance measured from the surface of the water to some point below the water. In the figure below, the depth between the center of the boat and the bottom of the lake is shown.

Shapes are another context in which depth is used. Two-dimensional shapes, only have a length and width. When a third dimension is added, it is referred to as depth (or height). Depth only has meaning based on chosen reference points. Using the example of a 3D shape, any of the lengths of the shape could theoretically be depth, based on the orientation or chosen reference.

In the figure above, the side labeled depth is more commonly referred to as height, but if the chosen reference point is the top of the rectangular prism, then the depth is the distance measured downward from that point to the bottom of the prism.

In this case, the reference point for the depth is the front of the page, and the distance measured "into" the page is the depth.

Depth vs. height

The International Organization for Standardization (ISO) defines depth and height as follows:

Depth The distance between a point and a chosen reference surface, measured downward and perpendicularly from the surface.
Height The distance between a point and a chosen reference surface, measured upward and perpendicularly from the surface.

The only real difference between the definitions is the point of reference and the direction of measurement. There are conventions for measurements of distance, but like in the shape examples above, there is some freedom on how to label various distances, as long as they are consistent and clear.