Gregory A. Lyzenga, a physics professor at Harvey Mudd College, gives this description:
Image: INTERNATIONAL METEOR ORGANIZATION
Meteor showers occur when the earth in its orbit around the Sun passes through debris left over from the disintegration of comets. Although the earth's orbit around the Sun is almost circular, most comets travel in orbits that are highly elongated ellipses. As a result, some comets have orbits that intersect or partially overlap the earth's path.
Because a comet's nucleus is made up of a combination of icy materials and loosely consolidated "dirt," when a comet is heated by passing close to the Sun, it more or less slowly disintegrates, producing the visible tail. The rocky debris, consisting of mostly sand-size particles, continues in an elongated orbit around the Sun close to that of its parent comet. When the earth intersects this orbit in its annual trip, it can run into this debris, which burns up on entry into the earth's atmosphere, producing a visible shower of meteors.
Image: MIKE COOP, California Meteor Society, NASA
Meteor showers associated with particular comet orbits occur at about the same time each year, because it is at those points in the earth's orbit that the collisions occur. However, because some parts of the comet's path are richer in debris than others, the strength of a meteor shower may vary from one year to the next. Typically a meteor shower will be strongest when the earth crosses the comet's path shortly after the parent comet has passed.