Plasma is the fourth state of matter—electrically conducting matter where electric current can flow freely. It is overwhelmingly the dominant component in the universe—stars and the matter between stars is made of plasma. Places like Earth and the other planets, where matter is mostly non-conducting, are the rare exceptions.
Fusion reaction take place in plasma, because any matter heated to high enough temperature becomes a plasma—most or all of the atoms have some of their electrons stripped off, so the electrons are free to move. Plasma physics is the study of matter in this state. While the phenomena of plasma physics can be understood in terms of the laws of electromagnetism, the theories of atomic structure, quantum mechanics and nuclear physics, there are many collective phenomena that occur in plasma that require intensive research on their own. This is especially of the main instabilities that plasma are prone to develop. An example is the filamentation instability that produces dense filaments of currents like those in the plasma focus device.
Plasma exists here on earth. Lightning bolts are plasma, as are flames. Many of us watch TV on plasma screens, where tiny pixels of plasma light up the screen. Neon and florescent lights are filled with plasma. The interaction between experiments with plasma in the lab and observations of much larger plasmas in space has been key to advancing this field.
For more on plasma physics go here.