Meteor showers are annual peaks in activity that occur when the Earth crosses a stream of debris left behind by another object, usually a comet. Many showers go through cycles of increased and decreased activity depending on how recently their parent body was near the Earth in its orbit. The Leonids are well known for this effect, with the parent body, Comet Tempel-Tuttle, having a 33-year period. Consequently, for a few encounters every 33 years the Leonids can produce impressive numbers of meteors, while it remains a fairly minor shower most of the remaining years.
Meteors that are part of a shower appear to follow paths that point back to a common point in the sky, called the radiant. That's because all of the meteors are traveling in the same direction when they strike the Earth's atmosphere, so the radiant is really just the vanishing point. If you've ever driven a car when it was snowing, you will have noticed the same effect, with the snowflakes appearing to come from a single point in front of the car. Meteor showers are named for the constellation that their radiant lies in.
This chart shows meteor activity as recorded over twenty years by the Cloudbait allsky camera. The major showers are very obvious, as is their uneven distribution throughout the year. The Leonids appear to be more active than they really are. That's because this data includes 2001 and 2002, when the Leonids were unusually active. In fact, the Orionids, Perseids, and Geminids are all much more active showers than the Leonids. As more data is added to this chart over the years, the Leonid peak slowly drops to its normal level.