What is a good example of leveraging the differences between int*_t, int_fast*_t and int_least*_t in C++11?

According to online documentation, there are differences in between these fixed width integer types. For int*_t we fixed the width to whatever the value of * is. Yet for the other two types, the adjectives fastest and smallest are used in the description to request the fastest or the smallest instances provided by the underlying data model.

What are the objective meanings of "the fastest" or the "smallest"? What is an example in where this would be advantageous or even necessary?