Actually, the Leonids are just for the one day.

Sure you can see meteors all the time, the reason they peak on a particular day in November is because we pass through the flight path of comet Temple-Tuttle, which essentially leaves a "slime trail" behind it.

If you looked at our orbit edge-on, you'd see that Temple-Tuttle's path is irregular and doesn't intersect our orbit perfectly every time. It's kind of like a shotgun blast. Some years we hit one of the "pellets" and some years we don't. They just predicted (accurately) that this November 18th would be better than most:



More information here.