I have been told that stone flooring is called non-resilient. What is the difference between resilient and non-resilient flooring?

Resilient flooring or tile is material that will return to its original shape after it has been compressed or stepped on. Examples of resilient floors are vinyl, rubber, cork, asbestos and linoleum.
Stone, quarry tile, terrazzo, ceramic, and concrete lack this resilient property and are therefore called non-resilient.

FYI There are many new materials available that simulate stone. Make sure you can tell the difference.