The Leonid meteor shower peaks on Tuesday, November 17. The Leonids are a highly variable shower, and as such are a bit of a gamble on what you'll see. Could be great, could be so-so. But, there are predictions of a few hour peak with perhaps 300 meteors per hour centered at about 1:45 p.m. Pacific time, which will be great for those in darkness at that time, particularly in pre-dawn hours occurring in Asia. For those elsewhere, the best time to view will probably be your local pre-dawn hours on the 17th. In any case, the good news is there should be no moonlight to interfere with the meteor shower.
The Leonids are caused by debris from comet Tempel-Tuttle. Each year, when Earth passes through the orbital debris trail left behind by the comet, we get an increased number dust and sand-sized particles hitting the upper atmosphere at very high speeds. As they vaporize, we get nice streaks of light crossing the sky -- meteors. But, each year, we pass through slightly different parts of past orbital debris left around by the comet. If we pass through a very "clumpy" part, we get lots of meteors.
They are named the Leonids because their trails will all point back to the so-called radiant in the constellation Leo. The meteors can appear all around the sky, but if you trace an imaginary line back along their trail, a true Leonid will intersect Leo.
The Leonids are particularly unusual with huge peaks every 33 years or so, but the last occurred only a few years ago. So, usually they now give about 20 meteors per hour, rating them a bit mediocre. This year, though, some astronomers are predicting hitting a bit clumpier region elevating it to a most excellent 300 meteors per hour right at the peak, and perhaps 50-100 per hour a few hours before and after. So, the question you have to ask yourself this year is, do you feel lucky? If you do, relax, stay warm, and stare at the sky under the darkest sky you can find.