Interdisciplinary science is important to the society for the same reasons that science is important to the society in general : it increases our state of knowledge, giving us the power to make better, educated decisions and to improve out lives. (reason one)
what is special about interdisciplinary science, is that it incorporates many sources of knowledge. For example an interdisciplinary study in history and geology can help us better understand human decisions in the past, given their climate and it can help us better prepare for climate change - this better preparation for the future is reason number two