A red sprite is a rare type of electrical discharge that can occur above a large thunderstorm. They can take on a number of different shapes and are usually red to orange. Sprites only last fractions of a second and are faint so are hard to spot with the naked eye. They rise between 50 and 90km above the Earth’s surface.
They are triggered by positive lightning between a cumulonimbus cloud and the ground. They were only first photographed in 1989. To capture them you need to have the right conditions. A dark clear sky and a good view of the atmosphere above a distant thunderstorm.
Unlike ordinary lightning, these electrical discharges are not high temperature, but are more like the discharges inside fluorescent light tubes.
Here’s a timelapse video showing some sprites, produced by Randy Halverson:
Other types of upper-atmospheric lightning are blue jets, blue starters, gigantic jets and ELVES. You can read more about them in this Wikipedia article.