Since 99% of the visible universe is made up of plasma, you won't have to go far to find plasma, which as you correctly guessed, is the fourth state of matter. You can find it by looking up at the sun, at a fluorescent light bulb that's turned on, or in a bolt of lighting. The explanation of plasma is not too complicated. When you melt ice into liquid water, the water molecules (composed of two Hydrogen and one Oxygen atoms) go from being confined in the crystalline solid state to being able to freely flow like they can in the liquid state. If you heat that liquid water up so that it boiled, you would form water vapor that makes up the gas phase where the water molecules can freely bounce around and have large spacing between them. I've just described the three states that you know of: solid, liquid, and gaseous. The fourth state, plasma, happens when you continue to heat up that water vapor so hot that the actual Hydrogen and Oxygen atoms that make up the water molecules are able to move independently from each other with large spacing between them just as individual vapor molecules were able to travel in the gaseous state.

A plasma is a state of matter in which all of the atoms are at least partially stripped of their electrons. To a first approximation, a plasma behaves like a very hot gas in that it expands to fill any container it may be placed in, but because it is ionized, it can also be directed around by magnetic fields, is a perfect conductor electricity (think "lightning bolt"), and is capable of generating its own magnetic fields. So, basically, you can think of the behavior of a plasma as being a very hot, gaseous magnet.

Plasma is a partially ionized gas, in which a certain proportion of electrons are free rather than being bound to an atom or molecule. The ability of the positive and negative charges to move somewhat independently makes the plasma electrically conductive so that it responds strongly to electromagnetic fields.

Everything we see is made of atoms. Atoms are made from protons, neutrons, and electrons. A plasma exists when the electrons are ripped out of the atoms. Plasmas can be caused either by high-energy collisions or by very high temperatures. Lightning is basically a plasma: a huge electrical current flows through the air, and it heats the air so much that it rips electrons from the air molecules. The electrons are then free to move as electricity. Plasmas are not always hot, though. Fluorescent lights emit light from a very weak plasma... and they're still pretty bright.