A plasma (or, more properly, an electromagnetic plasma) is a phase of matter that has enough energy for the electrons to separated from the nucleus. It consists of independently moving electrons and nuclei, and thus has some rather interesting properties, such as very good magnetic shielding. It can be found in places such as the center of the sun, and also, in small quantities, surrounding a lightening bolt.
Many people consider solid, liquid, gas and plasma to be the only four phases of matter. This is not true, as there exist many others, but they are generally more exotic with names like hadron gas or Bose-Einstein Condensate.