Removing just one organism from a food web is potentially devastating to an ecosystem. This is because organisms in a food web are interconnected and rely on one another for survival. If one organism is removed, all other organisms become threatened.
It may be helpful to use a specific example. Sea otters live in the kelp forests off the coast of the western United States. Sea otters eat urchins and other invertebrates. These invertebrates, in turn, eat kelp. If the sea otters are removed, then there is nothing keeping the invertebrate population in check and they begin to devour the kelp forest faster than it can grow back.
This means that the habitat of numerous fish and other animals that rely on kelp is destroyed and they become threatened. Furthermore, kelp absorbs a vast amount of carbon dioxide and therefore helps stall global warming. Therefore, removing just one organism, the sea otter, can have a drastic impact on both its own food web and also the entire planet. This is true of organisms throughout the world.
All organisms exist as part of food webs and all food webs exist in a delicate balance that all its members must participate in, lest that balance be disrupted.