It is a most commonly accepted rule of thumb that it is difficult to understand or visualize data represented in or by more than three dimensions.
Dimensional (-ity) reduction is the process of attempting to reduce the number of random variables (or data dimensions) under statistical consideration, or perhaps better put: finding a lower-dimensional representation of the feature-set that is of interest.
This allows the data scientist to:
Avoid what is referred to as the curse of dimensionality
Reduce the amount of time and memory required for the proper analysis of the data
Allow the data to be more easily visualized
Eliminate features irrelevant to the model's purpose
Reduce model noise
A useful (albeit perhaps over-used) conceptual example of...