What is a state of matter?
Essentially a description of the way that its particles are organised.
Particles packed tightly together such that they can vibrate but not move freely.
Particles can move fairly freely around, but the collection of them is more or less incompressible.
Distance between particles much greater than their individual size. Gases are compressible.
Like a gas, but able to conduct electricity. In this state of matter electrons are not tied to individual atomic nuclei, but are able to move around.
Apart from these four commonly observed states, there are non-classical low energy and high energy states, e.g. glass, liquid crystal, Bose Einstein condensate, superfluid, electron-degenerate, neutron-degenerate, and several more.