The air around us is always under pressure. All of the molecules of gas in the atmosphere are being pulled down by gravity. Near the edge of the atmosphere there are few molecules, and so the pressure is small. But close to the ground the pressure (weight) of all the molecules above causes the pressure to be much higher.
The average pressure of the air at the Earth's surface is 1000 millibars (1 bar, where bar is short for barometric pressure unit). Air pressure changes all of the time because the air in the atmosphere is continually swirling about. In places where air sinks - called high pressures or anticyclones - the pressure might be average air pressure + 40 millibars. In places where the air is rising (lows, or low pressures) the pressure may be 40 millibars lower than normal.
A device that pushes air molecules closer together is called a compressor (although people also commonly say 'pump' as well). Our lungs are used as a compressor all the time. Our muscles squeeze our lungs to push air out. Air only goes out because, by squeezing out lungs we put the air at greater pressure than outside our bodies. Then, when we relax our muscles, our lungs can expand. Now there is less air pressure in our lungs than outside, and so the air flows in again.
The molecules of air resist being brought closer together and so they push back on whatever is squeezing them. You can see this by simply blowing up a balloon.