An intrusion is magma (melted rock) which cools and becomes solid under the Earth's surface. By contrast, an extrusion is magma which cools into rock above the surface of the crust. Both intrusive and extrusive rocks are classed as igneous rocks.
The process of forming intrusive rocks may take millions of years. As the rock slowly cools into a solid, the different parts of the magma crystallize into minerals. The crystals are usually larger than in extrusive rocks. Many mountain ranges, such as the Sierra Nevada in California, are formed mostly by intrusive rock. Often they are huge granite (or related rock) formations.
Intrusions vary widely, from mountain range sized batholiths to thin vein-like fracture fillings. When exposed by erosion, these cores called batholiths may occupy huge areas of Earth's surface. Large bodies of magma that solidify underground before they reach the surface of the crust are called plutons.
Intrusive structures may go between bedding planes of earlier 'country' rock. That is a sill: an intrusion which makes a table along bedding planes. A dyke is an intrusion which moves up, crossing older strata.