Imagine a piece of pure semiconductor. Electrons in this bulk are free to move around, in three dimensions. In solid state physics, these electrons are sometimes referred to as an electron gas.
It is possible to constrain the movement of the electrons by disallowing one dimension -- that is, by reducing one degree of freedom. The electrons can then move freely in only two dimensions. A system of electrons confined to a plane is called a two-dimensional electron gas, or 2DEG.
Quantum wires have only 1 degree of freedom, and quantum dots have 0 degrees of freedom.
It is important to note that confinement is not perfect. A quantum dot is often defined as confinement to a very small volume of space, such as a sphere that has a diameter on the order of the material's Exciton Bohr Radius. At this size the energy bands of the semiconductor are no longer continuous, which results in the confinement.
Quantum confinement gives rise to many interesting effects, and these effects can be exploited to develop new semiconductor devices. One such type of device are mesoscopic devices, such as single-electron transistors.
Answered by:
Aman Ahuja, Physics Ugrad Student, WPI
'You cannot hope to build a better world without improving the individuals. To that end each of us must work for his own improvement, and at the same time share a general responsibility for all humanity, our particular duty being to aid those to whom we think we can be most useful.'