According to the Venerable Bede, Easter derives its name from Eostre, an Anglo-Saxon goddess of spring. A month corresponding to April had been named "Eostremonat," or Eostre's month, leading to "Easter" becoming applied to the Christian holiday that usually took place within it. Prior to that, the holiday had been called Pasch (Passover), which remains its name in most non-English languages.
(Based on the similarity of their names, some connect Eostre with Ishtar, the Babylonian and Assyrian goddess of love and fertility, but there is no solid evidence for this.)
It seems probable that around the second century A.D., Christian missionaries seeking to convert the tribes of northern Europe noticed that the Christian holiday commemorating the resurrection of Jesus roughly coincided with the Teutonic springtime celebrations, which emphasized the triumph of life over death. Christian Easter gradually absorbed the traditional symbols.
In Medieval Europe, eggs were forbidden during Lent. Eggs laid during that time were often boiled or otherwise preserved. Eggs were thus a mainstay of Easter meals, and a prized Easter gift for children and servants.
In addition, eggs have been viewed as symbols of new life and fertility through the ages. It is believed that for this reason many ancient cultures, including the Ancient Egyptians, Persians, and Romans, used eggs during their spring festivals.
Many traditions and practices have formed around Easter eggs. The coloring of eggs is a established art, and eggs are often dyed, painted, and otherwise decorated. Eggs were also used in various holiday games: parents would hide eggs for children to find, and children would roll eggs down hills. These practices live on in Easter egg hunts and egg rolls. The most famous egg roll takes place on the White House lawn every year.