Definition
The midnight sun is a phenomenon in high-latitude regions near the poles, where in summer the sun never fully sets, or the glow of sunset lasts all night so it never gets dark. You can see the sun even at midnight, which is why it's called the "Midnight Sun" in English. In Korean it's called baegya (白夜), meaning "white night," because the night glows white.
A tilted globe under a desk lamp
Picture spinning a tilted globe under a desk lamp. The top of the globe leans toward the lamp. No matter how much you twirl it, that part keeps getting bright light.
Earth is just like that tilted globe. Its axis (the imaginary line it spins around once a day) leans about 23.5 degrees from the straight-up line of its orbit around the sun. While Earth circles the sun over a year, the area around the pole in summer keeps its head bowed toward the sun all day long.
So even as Earth spins once a day, the sun can't sink below the horizon. This is the midnight sun: the sun circling above the horizon for all 24 hours. That's why the world stays as bright as noon even at night.
The view changes with latitude
The midnight sun only happens at high latitudes, far from the equator and close to the North or South Pole. The closer you get to a pole, the longer it lasts, from a few days to several months.
At 66.5 degrees north, the edge of the Arctic Circle, the sun stays up for just a day or two around the summer solstice. Near 70 degrees north, it lasts a bit over two months. At the North Pole, the sun hangs in the sky for about six months. Cities just below the Arctic Circle, like St. Petersburg in Russia or Helsinki in Finland, are different. The sun dips below the horizon for a short while, but it never gets truly dark.
Because the sun just skims below the horizon, red sunset colors and pale blue dawn light paint the sky all night. In these high-latitude cities, the name "white night" fits what you actually see.
A bit more precisely: the polar night, its opposite twin
To be a bit more precise, the midnight sun happens at the North and South Poles at opposite times, six months apart. When the Northern Hemisphere has summer and its midnight sun, the Antarctic Circle in the south gets the "polar night," when the sun doesn't rise at all. The closer to the pole, the longer and darker the polar night gets.
When winter comes to the Northern Hemisphere, the long darkness of the polar night begins in the Arctic. Meanwhile, the Antarctic Circle in the south gets sunshine all day long. It's a seasonal pair caused by Earth traveling around the sun while tilted.
During this time, people in Northern Europe cover their bedroom windows with thick blackout curtains to sleep, and they happily enjoy festivals that never go to bed. Thanks to this gift from nature, the magic of a tilted axis, Earth holds such a mysterious and varied mix of days and nights.
Common misconceptions
The midnight sun happens a little bit everywhere on Earth in summer.
A sun that never sets only happens at 66.5 degrees north or south latitude and beyond. A sun that sets briefly but leaves the night bright can also happen in high-latitude cities around 60 degrees, like St. Petersburg. Near the equator and at middle latitudes, summer still brings a normal dark night.
Where you meet it
In Nordkapp in northern Norway, the sun doesn't set below the horizon at all for over two months in summer (mid-May to late July).
In St. Petersburg, Russia, a bluish sunset glow lasts all night in mid-June, and the city holds its White Nights festival.
In one sentence
Because Earth's axis is tilted 23.5 degrees as it circles the sun, the sun doesn't set all night in the polar regions.