Metamorphic rocks are sedimentary rocks that have been altered drastically by tremendous heat and pressure -- as by being buried at very great depths for a long time, or being where they come into contact with molten magma. Metamorphic rocks usually show some banding, which is what remains of the distorted layers of the original sedimentary rock. This is a good feature to distinguish them from plutonic rocks, which usually don't have banding..
The most famous metamorphic rock is marble, a cut slab of which is shown at the left, nicely showing the typical banding. Marble forms when limestone and dolomite are metamorphosed.
Quartzite is common in some parts of the country because it is the metamorphosed form of the very common sedimentary rock sandstone. Quartzite is among the hardest, most resistant of all rocks.
Slate is the metamorphosed form of shale. As the picture at the right shows, it looks a good bit like shale. Hoever, it is much harder than shale and breaks with sharp edges. When slate is metamorphosed much more intensely than has been the case here, the resulting rock type, characterized by larger mica crystals, can be called phyllite.
Schist results from the very intense metamorphism of shaly rock. It is more deformed and recrystallized than slate. It is heavy, finely layered, dark, and contains many sparkly flakes of mica. I once had a friend in New York who took a geology class and all he could remember a few months after it was that "Long Island is full of schist." That's true, because it has been dropped there by glaciers bringing it down from farther north, but that's another story...