How does a comet change as it travels through space

Comets are like "dirty snowballs"; frozen gasses with dust and rocks in them. Each pass near the Sun causes the comet's nucleus to be exposed to intense sunlight, which causes some tiny fraction of the gas to evaporate and carry some of the dust and rock away into space. The gas and dust, near the Sun, cause the comet's "tail", and repeated passes cause dust and rock to spread out along most of the orbit of a comet. When the Earth enters one of these trails of old comet dust, we have meteor showers. 

On rare occasions, comets break apart or even more rarely, crash into planets. In 1994, the comet Shoemaker-Levy 9 broke apart and then collided with the planet Jupiter.