Hi haasfive,
This a "multicolor" slate. It is real slate tile in a custom mix put together by a local tile supplier. There are numerous varieties of this available from multiple manufacturers. Any high end tile store will carry something like it. It is also available in man-made ceramic that is a bit tougher and less susceptible to staining and scratching. Of course the man-made stuff doesn't look as genuine as the real thing.
Thanks for the question!
Bart