Leonid meteor showers and the Tempel-Tuttle comet
When material is shed from a comet, it mostly continues to follow the same orbit as the comet, but drifts out ahead or behind the comet in a complex way due to interactions with solar wind and the gravity of other objects.  

If you imagine the elliptical orbit of 55P/Tempel-Tuttle, it will have patches of denser dust in clumps spaced out around the ellipse corresponding to different perihelion approaches.  The 1466 clump will be in a different place than the 1500 clump, and they will both be travelling more or less around the comet's orbit.  

Since the comet's orbit only crosses Earth's at one place, and we only cross that spot once a year, we will only encounter whatever clumps of dust happen to be at that point at the same time the Earth is.

Calculating exactly where these clumps of comet dust are is non-trivial.  And that is a big reason why predicting how good a meteor shower will be is a rather tricky business.