Plants and animals need to coexist in order to thrive. Plants need animals just as much as animals need plants. A simple example of this would be trees. Trees provide many things to many different organisms but I will use shelter as an example. Trees provide shelter to many animals such as birds, so in essence they protect birds. Birds eat plants and in turn spread the seeds which grow. Insects, like bees, collect pollen from the flowers, etc. It is all part of a complex system in which species all depend on one another for some specific reason. So, interdependence is when plants and animals depend on each other for survival.
Organisms are interdependent by all taking part in a food chain. But other types of interdepency are symbiosis, mutualism and commensalism. Animals take in oxygen and give carbon dioxide: plants do the opposite.
Many plants exchange nutrients with fungi. In interdependencies, there is often a host and an associate. Beyond these types of inter and intra relationships among organisms are the more social interdependencies such as ants or bees working together for a common goal. And of course, there are humans who are inter and intra dependent: they rely on animals for food, plants for oxygen; and amongst themselves, humans rely on each other for goods, services, friendship, etc.
In general, the interdependency of organisms extends ecologically to their environment. Organisms rely on each other to sustain the ecological environment, something that humans have been lacking in. So, in general, organisms are interdependent because they have no choice. There are more particular instances (mutualism, symbiosis, etc.) where the connection is more local and direct. But in general, we're all part of the same ecosystem (Earth) and therefore, interdependent to certain degrees. For example, if we are dependent on wheat and something affects the climate on the other side of the world which causes a drought in the midwest, that shows an interdependent connection.