Low detail definition:
Plasma is the 4th state of matter, beyond solid, liquid and gas. It is a collection of positively and negatively charged particles whose numbers are approximately equal.
A plasma is a very hot gas, where some or all of the atoms are separated into ions & electrons. As the negative and positive charges are free to move, plasma is an excellent conductor and is influenced by magnetic and electric fields. Most space plasmas have a very low density, for example the Solar Wind which averages only 10 particles per cubic-cm. Inter-particle collisions are unlikely - hence these plasmas are termed collisionless.
Examples of solar system plasmas include :
Injections of plasma from the tail of the magnetosphere manifest themselves in impressive auroral displays near the planet's poles, where the accelerated charged particles interact with the Earth's atmosphere.
Auroral displays are also produced in the polar regions by solar wind plasma entering the magnetosphere on the dayside, through the process of magnetic 'reconnection' or 'merging'. During the process, particles are energised sufficiently to power auroral emissions. These dayside and nightside processes are associated with the transport and circulation of magnetic flux within the magnetosphere.
Contained by the magnetic field of the Earth, within this magnetosphere, are the Van Allen radiation belts - regions of enhanced energy, increased density plasma populations which pose danger to satellites & human spaceflight.
Another good description of the magnetosphere is found at the University of Oulu, Finland.
Francis Chen, Intro. to Plasma Physics, Plenum Pr., 1974
"A plasma is a quasineutral gas of charged and neutral particles which exhibits collective behavior" T. Boyd and J. Sanderson, Plasma Dynamics, Barnes & Noble, 1969
"A plasma is any state of matter which contains enough free, charged particles for its dynamical behavior to be dominated by electromagnetic forces." G. Parks, Physics of Space Plasmas, Addison-Wesley, 1991
"A plasma possesses properties that arise from both the individual interactions of the charged particles and those that come from the 'collective' behavior of particles. This behavior arises from many particles interacting simultaneously through the long-range Coulomb potential. The collective interactions are best described by the concepts of statistical physics."