Biomimicry literally means to imitate (mimesis) life (bios). The discipline is based on the idea that nature has evolved over billions of years, and the results of that evolution are incredible, ingenious systems that human design could learn and benefit a lot from studying. Nature has a way of functioning and innovating without harming the environment around it that human design could stand to emulate.
The above link provides a slideshow that gives a look into exciting projects that are being explored in this arena. Everything from solar panel coatings that imitate a moth’s eye’s ability to reflect light to adaptable building coatings that mimic human skin’s regenerative qualities can be seen in the slideshow, each complete with description.