The article How Tire Pressure Gauges Work explains air pressure. The atmosphere is about 50 miles "deep," and at sea level it exerts 14.7 pounds per square inch (psi). Our bodies think 14.7 psi is completely normal.
When you blow up a tire on a car or a bike, you use a pump to increase the pressure inside a closed space. A car tire typically runs at 30 psi, and a bike tire might run at 60 psi. There is no magic here -- the pump simply stuffs more air into a constant volume so the pressure rises.
A plane flies at about 30,000 feet. The air pressure at 30,000 feet is significantly lower than at sea level (4.3 psi versus 14.7 psi). High-pressure air is used to "pump up" the cabin in much the same way that a tire is pumped up. The high-pressure air on most planes comes from the compression stage of the jet engines.
Here are some interesting links: