Here's what I've dug up so far:
"In many ancient cultures, eggs were a common symbol (of) new life and immortality. In medieval times, Christians adapted the egg to their own religious devotions by giving up the eating of eggs during Lent and resuming it after Easter. Eggs came to represent the Lord's resurrection -- just as Christ broke out of the tomb on Easter morning, the yolk of the egg breaks out of its shell when cracked. The decoration of eggs for Easter is part of the folk traditions of many clutures, although it has little orno religious significance any more."
This is also why Easter baskets are so big. They were used to celebration of the end of Lent. Whatever was given up on Lent was put in the basket, such as eggs, candy or coffee to make it an even more celebratory day.
This is basically what I explained to our kids while we were decorating our eggs for our neighbors yesterday. I just used the Egg to symbolize Jesus burial (putting the egg in the dyed water) and then the new life (the egg coming out of the water brand new).
We're not trying to "spiritualize" these little things, but we can certainly teach our kids Christian values and meanings behind everything we do, because as you can see, there once used to be real, true meanings behind a lot of the generational traditions that we have taken part in since we were children ourselves.