Upward pressure in economics usually refers to increasing pressure on prices because of strong demands or shortage of supplies.
If supply is greater than demand, sellers will cut the price until consumers start buying. In this way, a surplus of a product puts downward pressure on its price.
It also puts downward pressure on supply. For example, if beef is not selling briskly—if there's a surplus of it on the market—what are producers going to do? They are going to raise fewer cattle. They'll shift the resources to raising sheep or maybe hogs.
Maybe some ranchers will get out of the business. Whatever it takes, that surplus quantity of beef will be taken off the market for the simple reason that consumers don't want to buy that quantity of beef at the price suppliers want for it.
The excess supply will dwindle until the quantity supplied equals the quantity demanded—at a price both consumers and producers can live with.
If we turn the situation where we have a shortage of beef, the market is demanding more beef than the quantity that producers are supplying, that results in a shortage, which puts upward pressure on prices.
How? When sellers see that they are constantly running out of beef before the next delivery, they know they can raise the price of the stuff. Consumers, in effect, are bidding up the price. When the price starts increasing, producers start producing more beef. They send their cattle to market sooner, and they move resources away from raising sheep and into raising cattle. If it's a long-term trend, more people may take up cattle ranching.
Again, whatever it takes, that shortage of beef will disappear as the price rises and the higher prices bring more beef to market. How much more beef will come to market? Enough to bring the quantity supplied equal to the quantity demanded again, at a price both consumers and producers can live with.
To know more, see Supply, Demand, and the Invisible Hand: Equilibrium: Mr. Demand, Meet Mr. Supply from Infoplease.com.