The Siberian Tiger is just one of thousands of animals that are on the edge of extinction. Each species is unique so if a species were to be wiped out, then this would interfere with nature's order.
For example, the elephants clear large areas of forest to allow light hungry plants to grow. These plants are an important food source for grazing animals. Wells dug by elephants are also used by animals that need a water source. So if the elephant were to disappear, then the animals that depend on the elephant would be wiped out too.
Natural extinction isn't a bad thing, it's a part of nature. But humans have been speeding up the process of extinction by cutting down trees, polluting the air, and littering. So humans also play an important part in speeding up the process of extinction.