The term that describes an igneous rock that forms quickly on Earth's surface from cooling lava is extrusive.

Here's why:

* Extrusive igneous rocks form when magma (molten rock) erupts onto the Earth's surface as lava and cools quickly. This rapid cooling leads to the formation of fine-grained minerals, often with a glassy texture.

* Intrusive igneous rocks, on the other hand, form when magma cools and solidifies underground. This slower cooling process allows for the formation of larger crystals.

So, examples of extrusive igneous rocks include basalt, rhyolite, and obsidian.