Comets

Didn't take this picture! But come in, read about comets :D

This is a picture of the comet Hyakutake, it entered Earth's orbit in 1996. 

Comets are some of the most interesting objects in solar systems for a number of reasons, including the fact that they are the source of all the meteor showers that we experience on Earth. 

First of all, its worth describing the difference between comets and asteroids. They exist amongst planets and moons as the four main types of objects in our solar system. When the solar system formed as a large, spinning disk of matter (hotter on the inside, colder near the outside), not everything could make it to be as big as planet, or even a moon. On the inside, the hot rocky material left over eventually would form the asteroids, and on the outside, the colder, icy material would form the comets. Think of comets as an asteroid-snowball. 

Anways - as comets approach the sun from the outer solar system they resemble asteroids, until they get close enough. As you can see in the picture, a cometary tail forms. This tail is made up of two different tails (as pictured), a dust tail and an ion tail.

The DUST tail (which is the one rising up towards the top of the photo) is pushed off of the comet due to the sun's radiation. It is free to flow about space as it may. 
The ION tail, (which is the one going straight back in a line, horizontally) is caused by the solar wind's charged particles reacting with and sweeping away the neutrally charged particles in the comet's nucleus. The ion tail always points directly away from the sun, even when the comet is on its way out of the solar system. This looks pretty weird, actually.

Now on to meteor showers - when a comet passes through Earth's orbit, the debris in the tail lingers for a very long time. When the Earth passes through the debris, its gravity attracts a lot of it, and when it falls into our planet's atmosphere, we see it streaking along the sky as it burns up into nothing.

It's also worth noting that usually all the shooting stars you see are incredibly dense pieces of space rock the size of a grain of SAND.