The inclusion of rabbits and eggs in the celebration of Easter is a combination of paganism, religious superstition, and practicality. Note that it is also marked by much speculation on the part of historians.
Where did the Easter Bunny and Easter eggs come from?
Spring was the season in which ancient peoples in the Northern Hemisphere shook off the cold dark days of winter, ate the last of their old, dried food, and started worrying about the fertility of their food sources. When knowledge of Creator God was unknown and the ways of nature mysterious, it was standard practice to assume a super-natural deity had control over the crops and livestock—and that people who wanted healthy crops and fertile livestock needed to earn this deity's favor. According to the 8th-century monk Bede, in the Germanic region this goddess was Ostara—Eostre in Old English—perhaps derived from the ancient goddesses of dawn, including Eos, Aurora, and Ushas. Bede recorded that as Christianity spread, the feasts in honor of Ostara gave way to the Christian Pascha celebration (Pascha being the Greek word for Passover and used in reference to the celebration of Christ's resurrection), but kept the name. Some have doubts that Bede's work is authentic, claiming that Bede made up the goddess Eostre, but Bede's writings give the only significant clue as to how we got the word "Easter".
If she existed in Germanic thought, as a fertility goddess Eostre was associated with hares and eggs. Hares were also companions to the Greek Aphrodite and the Norse Freyja, both goddesses of love and fertility (among other things). As hares and rabbits are extremely fertile, it's easy to see why they would become symbols of the season. But the Roman Catholic Church may have had another motive. Ancient legend claimed that hares are so fertile they can propagate asexually. The idea of an entire species that is prone to virgin births would be intriguing, and carvings of hares on various Catholic cathedrals led to speculation that the rabbit was a symbol of the Virgin Mary.
Beyond the idea that eggs represent fertility, there was a practical reason for parents to leave eggs for their children to find on Easter morning. Easter Sunday was the end of Lent—a 46-day fast from rich foods, including dairy, fats, meat, and eggs. Families with chickens would have 46-days' worth of eggs, many of them inedible or hard-boiled for storage. Using the eggs for games would be perfectly reasonable. In addition, the sealed egg with the treasure inside is used to teach children how Jesus was sealed in the grave.
It is often difficult to separate pagan symbolism from culture. Rabbits and eggs were pagan symbols of fertility, but they were also deeply ingrained in the native celebration of springtime. Whether a believer chooses to incorporate them into their Easter celebration is completely a matter of personal conviction. Bunnies and eggs hold no spiritual power; they are not demonic. Few today would confuse an Easter bunny with Aphrodite, Freyja, or Ostara-worship. If Easter bunnies and eggs help children value the day before they can fully comprehend Christ's sacrifice and victory, that's not a bad thing. If the controversy over using ancient pagan symbols causes too much concern, we are free to ignore them. Easter is a celebration of our freedom in Christ. That freedom extends to the use of bunnies and eggs.
Easter origins - What are they? Should we even be celebrating Easter?
How do we determine the date to celebrate Easter?
Why is the reality of the bodily resurrection of Jesus so central to the Christian faith?
Passion Week - What is it?
What is the passion of Christ?
Truth about Christianity