Effects on the environment when species extinct?

If a species goes extinct, anything it used to eat (be it plants or animals) now has one less predator and their numbers will increase. If they increase too much unchecked by their predators they may use too many resources and cause their own starvation. Another animal may start eating them, though -- since now they don't have to compete with the old species anymore.

Also, any animal which was a predator to the now-extinct species has lost a food source. They may have to find something else to eat or starve themselves into extinction, too.