A fine-grained igneous rock is a rock that is formed by melted magma cooling so quickly at the surface of the Earth that only tiny crystals form, most too small to be seen with the naked eye. Basalt is an example of such a rock.
When melted magma cools, igneous rock forms. When the magma cools at the surface of the earth, it cools more quickly and forms extrusive igneous rocks, which have a finer texture. When it cools slowly beneath the Earth's surface, intrusive igneous rocks form. These rocks have large crystals. Granite is an example of intrusive igneous rock.