A pluton is a deep-seated intrusion of igneous rock, a body that made its way into pre-existing rocks in a melted form (magma) several kilometers underground, in the Earth's crust. At that depth, the magma cooled and crystallized very slowly, allowing the mineral grains to grow large and tightly interlockedtypical of plutonic rocks. Shallower intrusions may be called subvolcanic or hypabyssal intrusions.
If a pluton is exposed at the Earth's surface, that means its top has been removed by erosion. It may represent the deep part of a magma chamber that once fed magma to a long-vanished volcano. Or it may represent a magma chamber that never reached the surface. The only way to tell the difference is by mapping and analyzing the details of the rocks that are exposed, along with the geology of the surrounding area.
"Pluton" is a general term that covers the whole variety of shapes taken by bodies of magma. That is, plutons are defined by the presence of plutonic rocks. Narrow sheets of magma that form sills and igneous dikes may qualify as plutons if the rock inside them solidified at depth.
Other plutons have fatter shapes that have a roof and a floor. This can be easy to see in a pluton that was tilted so that erosion could cut through it at an angle. Otherwise, it may take geophysical techniques to map the pluton's three-dimensional shape. A blister-shaped pluton that raised the overlying rocks into a dome may be called a laccolith. A mushroom-shaped pluton may be called a lopolith, and a cylindrical one may be called a bysmalith. These have a conduit of some sort that fed magma into them, usually called a feeder dike (if it's flat) or a stock (if it's round).
There used to be a whole set of names for other pluton shapes, but they aren't really much use and have been abandoned. In 1953, Charles B. Hunt made fun of these in USGS Professional Paper 228 by proposing the name "cactolith" for a cactus-shaped pluton: "A cactolith is a quasihorizontal chonolith composed of anastomosing ductoliths whose distal ends curl like a harpolith, thin like a sphenolith, or bulge discordantly like an akmolith or ethmolith."
Then there are plutons that have no floor, or no evidence of one. Bottomless plutons like these are called stocks if they are smaller than 100 square kilometers in extent, and batholiths if they're larger. Wikipedia has a list of prominent batholiths around the world: there are only a couple dozen. In the United States the Idaho, Sierra Nevada and Peninsular batholiths are the largest.
The formation and fate of plutons is an important, long-standing scientific problem. Magma is less dense than rock and tends to rise as buoyant bodies. Geophysicists call such bodies diapirs ("DYE-a-peers"); salt domes are another example. Plutons may readily melt their way upward in the lower crust, but they have a hard time reaching the surface through the cold, strong upper crust. It appears that they need help from regional tectonics that pulls the crust apartthe same thing that favors volcanoes at the surface. Thus plutons, and especially batholiths, go along with subduction zones that create arc volcanism.
For a few days in 2006, the International Astronomical Union considered giving the name "plutons" to large bodies in the outer part of the solar system, apparently thinking that it would signify "Pluto-like objects." They also considered the term "plutinos." The Geological Society of America, among other critics of the proposal, sent a quick protest, and a few days later the IAU decided on its epochal definition of "dwarf planet" that banished Pluto from the register of planets. (See What Is a Planet?)