�T�he way a gas like air exerts pressure inside a container like a tire or a balloon is through the action of the air atoms colliding with the sides of their container.
Imagine that you have a single atom of nitrogen in a sealed container. That atom is in constant motion ricocheting off the sides of the container. The speed of the atom's motion is controlled by the temperature -- at 0 degrees Kelvin (absolute zero) the atom has no motion, and at higher temperatures the speed increases. By its collisions with the sides of the container, the atom exerts an outward pressure. So there are two ways to increase the pressure inside the container:
Raise the temperature of the atoms inside the container - The hotter the atoms, the faster they move.
Put more atoms in the container - The more gas atoms you put in the container, the more collisions you get and the greater the pressure they exert on the sides of the container.
When you blow up a tire on a car or a bike, you use a pump to increase the pressure of the air inside the tire by increasing the number of atoms inside the tire. A car tire typically runs at 30 psi, and a bike tire might run at 60 to 100 psi. There is no magic here -- the pump simply stuffs more air into a constant volume, so the pressure rises.