The cone of depression is a term applied to a depression which forms in a groundwater table that has the shape resembling a cone. This conical depression forms around a well as a result of extracting water from the well at a given rate.
To better understand this, consider the following comparison:
If one places a straight long open and empty tube into the ground that runs from the surface into the water table which extends 3 feet into the water table, water will fill the bottom portion to a level of 3 feet. This is a very natural way in which water would fill such a tube.
In contrast, if this tube was to serve as a well where water is forcefully drawn from the water table to the surface, then this negative pressure will impact on the surrounding area which is in close proximity to the water table to transform its shape to become downwardly conical around the terminus of the well.
a pumping well creates a cone of depression that lowers an adjacent water table below the level of a stream or lake ... leaving an area where the water table dips down to form a cone shape. (NY Environmental Conservation)
The provided resource can be used to visualize this dynamic in greater detail.