The Leonids are a meteor shower. They are called the Leonids because they appear to radiate out of the constellation Leo. Its typical size ranges from that of a grain of sand to that of a pea. A meteor appears when it enters Earth's atmosphere and burns up high overhead. Meteors can be seen on any night, but Earth enters clouds of particles several times each year and the result is a meteor shower.
All meteors appear as brief streaks of light moving a short distance across the sky.
Some meteors move slow and some move fast. Here is a video of a bright, slow meteor. Note that a streak persisted for a little while after the meteor vanished. The Leonids are fast meteors and they leave lots of trains. For comparison an Indy race car can reach a top speed of about 250 mph, the fastest jet has a top speed of 2190 mph, and an orbiting spacecraft has an average speed of 20,000 mph.