Every year, between November 6-30, Earth sweeps through a stream of debris left behind by Comet Tempel-Tuttle. The number of meteors increases as the Earth moves deeper into the stream and reaches a peak on the night of the 17th. As the radiant, the point in the sky that the meteors can be traced back to, is inside the constellation Leo, this is called the Leonid meteor shower.
Most meteoroid streams contain only minuscule bits of dust and ice. However, the stream for the Leonids also contains many gravel-sized bits. This produces some very bright meteors in the night sky.
The Leonid meteor shower only produces around 15 meteors per hour, on average. Occasionally, usually shortly after Comet Tempel-Tuttle makes a pass around the Sun, the Leonids can deliver a meteor storm, with hundreds of meteors streaking through the sky every hour. According to experts, such a storm is not expected again until 2033 or 2034.
Leo is rising around 11 pm on the 17th and is fully visible by 2 am on the 17th-18th. The peak of the shower is actually 5 AM on the 17th, so the predawn hours on Saturday are the best viewing time. The Moon is two days past First Quarter on the 17th this year, so there will be some competing light in the sky, which will wash out the faintest meteors. However it will certainly be worthwhile to check the peak out on the 17th. It will definitely be worth it to get out to see the brightest of them, though! Bruce Fryer, Scott Harlow, and I were at the observatory last night and saw a few early arrivals which were quite impressive.