Dictionary.com defines a facet as "one of the small, polished plane surfaces of a cut gem." and faceting as "the act of cutting facets."
While this is an accurate definition, it's not the most illuminating one as to the How or the Why of transforming a dull rock into a sparkling and beautiful gemstone. And even then, the How and the Why of cutting flat planes onto a stone has changed a great deal depending on when you are asking the question.
However, each method needs to satisfy the same basic requirements:
A method of holding the stone
An abrasive to provide the cutting action
A way to locate the stone to place facets in the desired location