Definition
An arch is a way of building that guides a heavy load from above along a curve, spreading it out to the sides and down into the ground. The stones lock tightly against each other and hold together without glue or steel bars.
How stones hold each other up by pushing
Hold a slice of watermelon upside down and squeeze it firmly from both sides with your palms. It won't fall. An arch stands for the same reason. Cut stones into wedge shapes and stack them in a curve. The harder gravity pulls the stones down, the harder they press against each other.
The weight from above doesn't crush the stones. It closes the gaps between them and binds the whole structure together more tightly. The last stone, set in at the very top, is called the keystone. The moment it drops into place in the middle, every stone on both sides locks together with no gaps, and the arch can carry a huge bridge or ceiling.
Holding things up by being pressed is called compression. Stone and brick can crack easily when pulled apart, but they are extremely strong when squeezed. The arch is a technique that uses this trait of stone to the fullest.
Stopping the arch from spreading outward
You don't feel it when you walk across an arched bridge, but an arch is actually straining to spread its legs apart. The weight from above travels down the curve and turns into a force that pushes the base of each column outward.
Physics calls this force lateral thrust, or horizontal thrust. If the columns can't resist this push and slide outward, the keystone at the top slips down and the whole structure comes crashing down.
That's why ancient Roman and medieval builders packed very thick walls or mounds of earth against the outside of the columns to hold them in place. The flying buttresses that stretch out like wings from the walls of tall cathedrals do the same job: they push firmly from the outside so the arch can't spread sideways.
A bit more precisely
To be a bit more precise, almost no tension (the force that pulls a material taut) builds up inside an arch. Put a heavy load on the middle of a flat wooden plank or stone slab, and it bends downward like a bow. The bottom side gets pulled apart. Stone is very weak against this pulling force and snaps quickly.
An arch built in a curve that matches its load, on the other hand, turns that weight into almost pure compression. Hold a chain by both ends and let it hang naturally. Flip that sagging curve upside down, and you get the ideal arch shape, where only pushing forces are at work.
This principle is why aqueducts and temples built 2,000 years ago in Roman times still stand without steel bars. Some, like the Pont du Gard aqueduct, are made of stones locked together without mortar. Others, like the Pantheon, are made of Roman concrete. Today the same principle has been developed further and is widely used in arch bridges over long rivers and in the domed roofs of huge indoor arenas.
Common misconceptions
An arch only stays up if you smear thick glue or cement between the stones.
Some Roman arches, like the Pont du Gard aqueduct, have stood for nearly 2,000 years with no glue. Only the wedge shape of the stones and the locking force created by gravity (compression) hold them together.
An arch just needs to support the weight pressing straight down from above.
As the load travels down the curve, it creates a horizontal force that pushes the columns outward. So arches need something to hold the sides in, such as buttresses, solid ground, or iron tie rods.
Where you meet it
The Pont du Gard, a Roman aqueduct in France built 2,000 years ago from stones locked together, still standing grandly today
The dome of the Pantheon in Rome, which covers a huge space with no columns (it's an arch spun all the way around, built from Roman concrete with no steel bars)
An eggshell: it's thin, but it doesn't break easily when you squeeze it in your whole palm, thanks to its curved shape
In one sentence
An arch spreads the weight from above along a curve, so the stones press tightly against each other and hold themselves up.