There is an engineering term known as "system of systems." This refers to the way in which individual components and networks, when combined under one roof, become a new, more holistic system in which the whole becomes greater than the sum of its parts. The biosphere -- composed of the lithosphere, the atmosphere and the hydrosphere -- is a "system of systems." It is the sum of all the components and networks that comprise the planet. If just one of those components or networks fails, the reverberations are felt throughout the whole system.
Earth, unique among all known planets (a number that was until very recently constantly growing), is a fragile biosphere supporting life as we know it. That biosphere is composed of numerous ecosystems, each threatened by human interaction with the environment. As species become endangered and extinct due to over-hunting, over-fishing, destruction of habitats by people seeking to develop land for commercial use or for subsistence farming, and from global climate change caused by the depletion of the ozone layer of the stratosphere, ecosystems are destroyed. The more ecosystems that are destroyed -- think about the danger to coral reefs in the world's oceans due to man-made activities, and the role of those reefs in supporting chains of life -- the more endangered becomes the biosphere.
Biodiversity is an essential component of ecosystems, and of the system of systems, the biosphere. Plant diversity is essential to the survival of many insect and animal species, which are in turn essential to other animals. Animal diversity is vital in the sense that each species serves a purpose, whether that purpose is to control the growth of other animal species through hunting, or for the beneficial aspects of plant-animal interaction (for example, as honey bees become endangered, the effects on those types of plants with which they interact will be catastrophic for those plants, which will, in turn, threaten the survival of more species of insects). The oceans, as mentioned earlier, represent a very complex and vitally important component of the biosphere, and yet are constantly under threat from commercial fishing, industrial pollution, and changing temperatures associated with climate change. It's all a system.