What is the general term for igneous rock that forms from cooled lava on the Earth's surface?

Extrusive

Extrusive rocks form when magma reaches the surface as lava and cools rapidly, often resulting in small mineral crystals or a smooth, glassy appearance. A famous example is obsidian, which cools so quickly that crystals cannot grow at all. You can remember the term because these rocks "exit" the Earth's interior to solidify on the surface.