It's a little difficult to appreciate how significant the changes in pressure within the atmosphere can be. The following experiment is a fun way to get a good general idea.

Go to a high altitude, like a mountain summit. Take an empty plastic water bottle and remove the cap so it fills with air with a pressure at that altitude. Now put the cap on tightly so it seals in that air. Then go down in altitude. The air inside stays at the lower pressure of the higher altitude. The outside air pressure will increase as you descend. If you can change altitude enough, the bottle will get crushed!

Most pressure sensors work in a similar way. They have a sensing membrane which is like the plastic bottle. Here is what the inside of a sensor similar to the BMP280 on the Adafruit CLUE looks like:

Think of the inside of the plastic bottle being like what is underneath that blue surface - a small pocket of trapped air. The upper side of the blue surface is like the outside of the bottle. It will see whatever air pressure it is surrounded by. So as the air pressure above the blue surface changes, it deflects, like the water bottle being crushed. This deflection is then sensed by the other electronics on the sensor. Turning that into pressure is just a matter of math.