The peacock was believed by the ancients to have flesh that does not decay after death, and thus became a symbol of immortality.
This symbolism was adopted into Christianity, and the peacock appears in many early Christian mosaics and paintings.
Because of the way a peacock struts and displays its feathers, the peacock is sometimes a symbol of human vanity.
The peacock is used in church decorations in the Easter season.
(from http://www.religionfacts.com/christianity/symbols/peacock.htm)