Here is a very short list of inventions of mankind which were made after being inspired by nature. The complete list would call for hundreds of web-pages (!)
Helicopter: Have you ever wondered that the helicopters resemble the exact design of a dragonfly! The design was improvised by observing the hovering of hummingbirds and sun birds.
Aeroplane: Hovering birds such as eagles, vultures, pelicans, albatrosses and terns look like the non-flapping planes during their flight patterns.
Solar panels: from the reptiles. The idea of using the sun as a source was kick-started by basking lizards and crocodiles.
Wind energy: Butterflies flapping their wings
Radio signals, radar, mobile phones: The bats use these for millions of years. So do the elephants which use the infrasonic signals to communicate over miles.
Sonar: The whales and dolphins use these to locate the food and mates.
Armored tanks and vehicles: Snails and tortoises are influential in these technologies.
There are many more scientific achievements that have been inspired by natural elements. Try and find them and have fun.