A mass of rock which forms underground is under enormous pressure because of the material on top. As geological processes bring the rock to the surface, the material pressing down on is is slowly removed by processes of erosion. When the rock is finally exposed, all the pressure that has been keeping the rock in check has been removed.
Now, plutonic rock isn't a particulary plastic substance, and the rock will not slowly expand under release of pressure, it will break. In particular, stress fractures will form parallel to the surface of the rock. When exposed to the elements, water will get inside the cracks and freeze, prying them open even further. When the water dries up, salt crystals grow in the cracks. These fractures eventually cause plate or leaf-shaped pieces of rock to break off.
Sometimes these plates are tiny, other times they are enormous. In July 1996, a 31,500-ton slab of granite fell off Glacier Point into Yosemite National Park's Happy Isles Visitor Center, killing a tourist. In 1999, a 25-foot long slab of granite fell off Panorama Cliffs into the Yosemite valley. This killed one climber and forced the evacuation of Curry Village, one of the park's principal campgrounds.
As a mass of rock continues to exfoliate, it takes on a rounded appearance. When such remnants are the size of mountains, they are called "exfolation domes", such as the ones in Yosemite Valley (although these have been modified into Half domes by valley glaciers which have ground half the mountain away).