How could the extinction of a species affect life?

The extinction of a species would mean the death of a species. Every species has its own niche (or role) in its ecosystem. For example:
Carnivores --eat--> Herbivores --eat--> Plants --get nutrition from--> Decomposers --eat dead things. It's an (albeit very small and simple) circle of life.
Now if the herbivores were to go extinct, so would the carnivores. If the carnivores were extinct, then the herbivores would eat all the plants until the plants were extinct, and then the herbivores would die of starvation. There's a balance to things that would be crumbled and ultimately, the ecosystem would be very negatively affected if not destroyed.

In addition, through studying other species, science can extend its knowledge. Some species have natural adaptations to problems that plague us humans. If science can figure out how those species deal with the problem, that solution could be modified to fit humans, too. If that species goes extinct, that possibility is lost.