The usual answer is this:  The outer part of the Earth is divided into a dozen or so rigid plates that are moving slowly across the Earth’s surface.  As they move, it is inevitable that some of the plates will collide.  Where two plates do collide, they push against each other causing the ground surface to rise and, thus, forming mountains. That, at best, is a partial answer.


The problem with this idea is that some mountain ranges have formed far from plate boundaries, away from the line where two plates are colliding.  Examples in North America include the Sierra Nevada of California, the Teton Range in Wyoming and the Adirondacks in New York.  A more complete answer to how these mountains formed is through a process known as delamination.


Delamination is the separation of a slab from the lower part of a rigid and dense tectonic plate down into a hot and viscous mantle.  It is similar to the dropping of ballast from a ship:  As the cold, dense slab separates, the upper part of the plate is more buoyant and rises, forming mountains.


That such slabs have separated are clearly revealed in images of the Earth’s interior made with seismic tomography.  Seismic tomography uses earthquake waves to image the Earth’s interior in the same way that X-rays are used to make CAT scans of the interior of the human body:  The speed of the waves changes depending on the density of the Earth’s interior.  Gather enough earthquake waves passing through the Earth’s interior at different angles and an image of the Earth’s interior—a seismic tomographic image—can be make.


Such images have revealed dense slabs that are separating and dropping from under the Himalayas in Asia, the Apennines in Italy and the Atlas Mountains in North Africa.  There are also slabs beneath the Basin and Range of Nevada.  At the western edge of the Basin and Range, a slab is currently peeling away and, as a result, the Sierra Nevada are rising.