Structured systems have binding energies larger than the ambient thermal energy. Placed in a sufficiently hot environment, they decompose: e.g., crystals melt, molecules disassociate. At temperatures near or exceeding atomic ionization energies, atoms similarly decompose into negatively charged electrons and positively charged ions. These charged particles are by no means free: in fact, they are strongly affected by each others' electromagnetic fields. Nevertheless, because the charges are no longer bound, their assemblage becomes capable of collective motions of great vigor and complexity. Such an assemblage is termed a plasma.
Of course, bound systems can display extreme complexity of structure: e.g., a protein molecule. Complexity in a plasma is somewhat different, being expressed temporally as much as spatially. It is predominately characterized by the excitation of an enormous variety of collective dynamical modes.
Since thermal decomposition breaks interatomic bonds before ionizing, most terrestrial plasmas begin as gases. In fact, a plasma is sometimes defined as a gas that is sufficiently ionized to exhibit plasma-like behaviour. Note that plasma-like behaviour ensues after a remarkably small fraction of the gas has undergone ionization. Thus, fractionally ionized gases exhibit most of the exotic phenomena characteristic of fully ionized gases.
Plasmas resulting from ionization of neutral gases generally contain equal numbers of positive and negative charge carriers. In this situation, the oppositely charged fluids are strongly coupled, and tend to electrically neutralize one another on macroscopic length-scales. Such plasmas are termed quasi-neutral (``quasi'' because the small deviations from exact neutrality have important dynamical consequences for certain types of plasma mode). Strongly non-neutral plasmas, which may even contain charges of only one sign, occur primarily in laboratory experiments: their equilibrium depends on the existence of intense magnetic fields, about which the charged fluid rotates.
It is sometimes remarked that 95% (or 99%, depending on whom you are trying to impress) of the baryonic content of the Universe consists of plasma. This statement has the double merit of being extremely flattering to Plasma Physics, and quite impossible to disprove (or verify). Nevertheless, it is worth pointing out the prevalence of the plasma state. In earlier epochs of the Universe, everything was plasma. In the present epoch, stars, nebulae, and even interstellar space, are filled with plasma. The Solar System is also permeated with plasma, in the form of the solar wind, and the Earth is completely surrounded by plasma trapped within its magnetic field.
Terrestrial plasmas are also not hard to find. They occur in lightning, fluorescent lamps, a variety of laboratory experiments, and a growing array of industrial processes. In fact, the glow discharge has recently become the mainstay of the micro-circuit fabrication industry. Liquid and even solid-state systems can occasionally display the collective electromagnetic effects that characterize plasma: e.g., liquid mercury exhibits many dynamical modes, such as Alfvén waves, which occur in conventional plasmas.