"A geological term meaning the rock native to an area."
Country rock is a geological term used to refer to whatever rock was in place before the process under discussion started. When you are talking about magma and lava, country rock is any rock that was there before the magma/lava intruded. When talking about metamorphism, country rock is the material being transformed. When talking about alluvium, the country rock is whatever the alluvium was deposited on. When talking about erosion, the country rock is what is being eroded.
Obviously, the country rock was formed from exactly the same processes as any other rock; it was simply formed at a much earlier time. This can result in some interesting turns of phrase, as when xenoliths in current rock formations are described as country rock. It is probably best to think of country rock as being the geological equivalent of foobar.