The difference between extrusive and intrusive igneous rock begins with the substance that gives rise to both: magma. Magma is a mixture of molten rock and gases that move beneath the earth's crust in a zone called the mantle, which is between the crust and the core of the planet. Sometimes magma cools and solidifies at the line between the crust and mantle where the temperature falls below the rocks' melting point. Sometimes the gas-filled magma -- under pressure in roughly the same way as bottled soft drinks -- finds an opening in the crust of the earth and explodes through the crust as a volcano.
The crust of the earth is divided into large plates, like great rafts that are pressed together on a sea of magma. These plates move. Plate boundaries along the sea floor create spreading -- or divergent -- boundaries. Plate boundaries that press together above sea level create crushing -- or collisional -- boundaries. Plate boundaries that slide against one another are called transform boundaries, and plate boundaries that slide over each other are called convergent boundaries. Collisional boundaries push the land up into mountains, the way a fold appears when you crush together a fabric. These boundaries force igneous rock that has cooled within the crust to the surface. Transform and convergent boundaries allow magma to explode free of the mantle, where the magma flows onto the surface of the earth then cools into a solid. Divergent boundaries on the ocean floor allow a constant flow of magma that cools under the water.
Extrusive igneous rock is rock that is formed when magma breaches the crust and cools on the surface of the earth. Because it cools quickly, it is usually very fine-grained, or smooth. Oftentimes, it still maintains the shape of a flowing liquid, with ripples and waves. The most common extrusive igneous rock is basalt. Divergent plate boundaries along the deep ocean floor also produce extrusive rock, which is then carried away from the boundary by the separating action of the divergent plates.
Mountains are made as a plate is crushed into folding. Intrusive igneous rock is rock that solidified along the crust-mantle plane; and it is pushed up to become the core of new mountains. Over time, as erosion changes the mountains, these intrusive igneous rocks are exposed. A great deal of the earth's surface is intrusive igneous rock. The most common intrusive igneous rock is granite. Intrusive rock is usually course-grained, because it has been mixed with pre-existing crust material called "country rock."