Interdependence is mutual dependence between things. If you study biology, you’ll discover that there is a great deal of interdependence between plants and animals.
Inter- means "between," so interdependence is dependence between things. We often use interdependence to describe complex systems. Marriage creates a state of interdependence between spouses. If your dog provides you with love and happiness, and you provide your dog with food and walks (and love and happiness), then your relationship with your dog is one of interdependence.