Although now Easter is commonly held to be a Christian celebration of the death and resurrection of Jesus, the original religious festival that was celebrated in the UK and other parts of the world was the festival of Ostara. This festival has been celebrated since around 1000 BC. A millennium before Jesus was said to have been born. (There is much debate about the actual birthdate of Jesus according to different traditions)
Ostara is a pagan goddess of fertility and therefore the celebration of Ostara is about birth, renewal and regeneration of nature.
We eat Easter eggs because eggs were used by the Celts during sacrificial offerings to Ostara and the goddesses of the moon, for example Freya. Eggs are symbolic of birth and renewal. Therefore eating eggs reminds us of the preciousness of life, that life renews and we thank Mother Earth for her glorious bounty.
The tradition of the Easter Bunny, again comes from Ostara. Ostara has the head and shoulders of a hare in many pictures of her. The hare is also a symbol of immortality and resurrection, because it is a nocturnal animal and sleeps during the day, to reawaken at night. Therefore Pagan's view the hare as sacred and historically it was forbidden to hunt the hare on feast days such as Easter and Imbolic.
Christianity came along later and when the missionaries came to convert the Pagans to the new religion, they clearly used some of the ideas from the Pagan faith to help with the transition so that it was familiar and compatible with the ideas from the old religion.