Equilibrium - a state of rest; state of balance; a position which, if attained, will be maintained.
Thus, an equilibrium price is one which, if attained in the market, will be maintained (until some disturbing factor causes a change in demand or supply conditions).
Note: equilibrium is a positive (as opposed to normative) economic concept. There is nothing inherently good or bad about equilibrium. It has nothing to with fairness.
Equilibrium exists whenever the quantity of a good demanded is just equal to the quantity of the good supplied. (Note: it is NOT when supply equals demand—it is when a point on the demand curve just touches a point on the supply curve.)
If the price of a good is above equilibrium, this means that the quantity of the good supplied exceeds the quantity of the good demanded. There is a surplus of the good on the market. The existence of this surplus gives sellers an incentive to lower their price, thus sending the price downward toward its equilibrium level.
Conversely, if the price of a good is below equilibrium, then it must be that the quantity of the good demanded exceeds the quantity of the good supplied—meaning that there is a shortage of the good (at the existing price). The existence of this shortage in the market gives sellers the incentive (and the opportunity) to raise their price. As the price rises, it is moving upward toward equilibrium.
Whenever the quantity of a good demanded at some price is just equal to the quantity of the good that sellers are supplying at that price, then there is neither a surplus of the good nor a shortage. Sellers lack incentive and opportunity to either lower or raise the price—it will be maintained. It is an equilibrium price.
Be able to illustrate graphically a below-equilibrium price, to explain what condition (relative to supply and demand-using proper terminology) exists to make this a non-equilibrium price, and explain and illustrate the adjustment process. Do the same for an above-equilibrium price.