So a buddy of mine recently started ranting about how planes shouldn't work. And im still not sure if hes kidding or just trying to get me to rant about science. Either way, I love ranting about science and thought this would be another great questions to answer as simply as I could.
So in our first terrible mspaint image, you have a bunch of air particles (if you dont already know, air is made of tiny little things called atoms), and a wing (we dont care about the shape just yet). The drawing is pretty bad, but imagine that the air particles are evenly spaced around the wing. The spacing of particles is called "air pressure" the more air particles there are packed into a space, the tighter they are together, the more air pressure there is because air particles like to be spread out. This is why in space movies if you open a window all the air goes rushing out, because there are NO air particles in space (or very very few at least) and LOTS of air particles inside for us to breath.
Our next image two images show the wing moving to the left, and a vacum is formed. This vacum is formed because we moved the wing closer to the particles on the left, but away from the particles on the right. Because of this, the space that the wing normally took up is empty, and the wing is started to bump into particles on the left.
Now the particles on the right are spacing out a bit more because they have more room. (because air particles like to spread out evenly) Imagine sitting on a crowed couch, and someone gets up. Everyone else will want to spread out a bit to be more comfortable. The area above and behind the wing now has a lower air pressure. No particles on the lower left of the wing have come into contact yet, so they are blissfully unaware of what is to come :)
Uh oh... the particles to the bottom left of the wing just got smushed. Now that they are all crammed together, underneath and infront of the wing has a higher air pressure, and because the wing moved again we have another vacuum behind/on top of it.
But this time some of the air from in front of the wing (at the top tip, just high enough over it to not get smushed below it) is going to get sucked downwards into the vacum. All particles that are near the vacum are going to get sucked into it. Except for the particles that are in front of/below the wing, because the wing is in the way.
So this keeps happening (not in steps like this, but continuously so that the vacum builds up more and more the faster the wing goes, and more and more particles get crammed together on the bottom of the wing. This difference in air particle spacing is the difference in air pressure, and because lower air pressures like to suck things into them, and higher air pressures like to press against things, the two work together to push the wing up into the air.
Vacum cleaners work because they push air particles out of a chamber, which creates lower air pressure inside. Because there is a higher air pressure outside the chamber, those particles want to spread out and rush to get inside and fill the chamber.
Balloons are a great example of high air pressure. The more air you put into a balloon, the more it presses against the rubber walls. If you keep putting more and more inside, eventually it will pop. But if you let go of the hole you were blowing into, you will see the air pushes very fast to get out. (This is because there is a higher pressure inside compared to the air outside.
So all in all, airplane wings work because they create more air pressure underneath the wing, and less air pressure above the wing, and the faster they go, the bigger the difference is, and the bigger the difference is the stronger the wing will be lifted.
Here is a nifty video to show it in real life, and in slow motion :)
A coworker reminded me that you can easily put your hand out of a car window while moving and see this effect for yourself by slightly tipping your hand up and down. (Make sure nothing is close to the side of the road so that you keep all of your hands/fingers) :)