All of the living organisms within an ecosystem comprise a living community. Within the living community are feeding relationships that are known as food chains. However, usually there are several interacting food chains tied together in what is known as a food web.
Consider the following food chain in a field. Leafy plants (producers) being eaten by--> grasshoppers ( primary consumer/herbivores) --> eaten by frogs (secondary consumer/carnivores) --> consumed by snakes (another carnivore- tertiary consumer)--> consumed by hawks (another carnivore and quartenary consumer).
If the frogs were to die off in this field perhaps due to a disease or due to pollutants, there will be an increase in the amount of grasshoppers feeding on the producers or green plants.
This can actually cause a major problem if the number of grasshoppers were to increase out of control. They eat plants and the number of plants,which are the basis of the food chain, could severely decrease which would impact all of the levels operating above this trophic level. The producer starts the food chain by capturing solar energy and producing chemical energy stored in the bonds of glucose.
You would also see an effect on the consumers of the frogs which are the snakes. They would lose an organism that they feed on which can cause their numbers to decrease.
However, since there may be several interacting food chains in the area at the same time, the number of grasshoppers in this question might not increase dramatically if predatory birds in the area were another consumer of grasshoppers. This is why a food web is a more realistic view of how feeding relationships occur in an ecosystem.
On the other hand, if an organism primarily eats one type of organism for food--which is pretty rare in nature, if the organism which is the food source were to die off this could lead to the extinction of the consumer of that organism. An example is the panda whose food supply consists of 99% bamboo. As bamboo forests are being cut down to use the wood to make furniture and other products, the pandas are losing their main food supply and thus may become extinct someday.