You should notice that shifts of the demand or supply curves push markets into disequilibrium that is either characterised by an excess demand (shortages) or an excess supply (surpluses).  It is this imbalance between the demand and supply that creates pressure for prices to converge towards equilibrium.  Overall, markets at any time will either be in a state of equilibrium or disequilibrium.  Any market in disequilibrium will have been caused by a shift to the left or right of the demand or supply curves (loosely speaking, increases or decreases of demand or supply).  The effects on markets can be summarised in the  four separate demand and supply diagrams.  

In each case, the market starts in equilibrium, with price at P1.  Then the market is disturbed by a change (or shift)  in demand  or supply which results in the existing price (P1) being either too low or too high.  The market is no longer in equilibrium as a price that is too high reflects an excess supply (i.e. a surplus) and a price that is too low reflects an excess demand (i.e. a shortage).  

When an excess supply develops (e.g. because of an increase in supply or a decrease in demand) normal market forces will force the price downwards.  The lower price results in more demand by consumers as they are enticed by a cheaper product (an expansion of demand along the demand curve) and less supply as producers are deterred by lower prices and profits (a contraction along the supply curve).  This expansion of demand and contraction of supply will continue to occur until the excess supply is eliminated and the price eventually rests at its new lower equilibrium price of P2.

Similarly, when an excess demand develops (e.g. because of a decrease in supply or an increase in demand) normal market forces will force the price upwards. The higher price results in less demand by consumers as they are deterred by a more expensive product (a contraction of demand along the demand curve) and more supply as producers are encouraged by higher prices and profits (an expansion along the supply curve).  This expansion of supply and contraction of demand will continue to occur until the excess demand is eliminated and the price eventually rests at its new higher equilibrium price of P2.