Black Potatoes is a generic term used for dark coloured potatoes, whether they be purple or blue skinned.
Generally, you can assume the flesh inside will be bluish or purplish as well, at least before cooking. Most tend to have their colour fade somewhat during cooking, though there are exceptions.
Most tend to be halfway between waxy and floury, meaning you've got a reasonable chance of their staying together for use in salads (but that is not always guaranteed), and that they can be mashed, though they don't make the best mash -- the interest is more in the colour instead of the texture.
They are usually best steamed rather than boiled, and don't overcook, as they will fall apart.