First, I'll need to explain a little about plasma in general: Plasmas are the fourth state of matter. Most people are aware of solids, liquids, and gases - each of these states of matter have various structures and densities based on the energy the molecules of the substance have and the innate chemical properties of the matter. Changing from one state of matter to another requires inputing or extracting energy from the system the energy is in; we commonly refer to these changing points as the Melting Point (changing from a solid to a liquid and vice versa) and the Boiling Point (changing from a liquid to a gas) of the substances in question.
In all of these states of matter, we generally have (using a classical model) electrons bound to the atoms in the molecule more or less permanently. In plasmas, however, (I'm talking about neutral plasmas right now - non neutral plasmas are slightly different), the temperature (and hence the kinetic energy) of the matter is high enough to separate the electrons from the atoms they are originally connected to permanently. The result is a gas-like substance with free floating nuclei and electrons.
Since most of matter we encounter in our daily lives is one of the three traditional states of matter (solids, liquids, and gases), it may come as a surprise (it did for me) that the majority of the matter in the universe that we know of resides in the plasma state. The sun, for example, is hot enough to keep the matter inside of it more or less constantly in the plasma state, and the space in-between consists of large amounts of plasma as well. Unfortunately (or fortunately for scientists like me :) ) since plasma is relatively rare on the surface of the earth, knowledge of the state of matter lags behind that of gases, liquids and solids, and plasmas constitute a heavy area of research in physics.
This post has already gotten rather long, so I'll leave it at this. Next Time: Non - Neutral Plasmas!