Rocks are divided into three categories: sedimentary, metamorphic and igneous. A lot of times these three classes are referred to as phases because each class can morph into each of the other classes over long periods of time. But that's can morph, it isn't automatic.
In English, those three classes can be pretty broadly defined like this: sedimentary rocks are formed by compacted sediment, metamorphic rocks are rocks that are transformed by heat and pressure after they're already formed and igneous rocks are formed by cooling magma. Some examples of sedimentary rocks are limestone and travertine. Some metamorphic rocks are marble, quartzite, soapstone and slate. Finally an igneous rock that's in a lot of peoples' homes is granite.
In the chart above, there's a delineation made between intrusive and extrusive igneous rock. Intrusive means that a formation of igneous rock rises into the earth's crust but doesn't break the surface. Not breaking the surface results in a very particular crystal structure. Extrusive igneous rock breaks the surface and cools quickly when not under pressure. This results in a different structure even if the magma has the same composition.
So there's my breakdown of the three classes of rock. There are examples of all three classes that end up being pressed into use by humanity and I'll be spending some time explaining them further. First up will be granite.