What does a butterfly symbolize?

It is said that butterflies are good luck. 

If one lands on your shoulder it is said to be a lucky sign. 

Butterflies are a symbol of resurrection, hope, joy, and new beginnings. It is a symbol of rebirth and a transformation of change freedom, growth and rebirth.

They are also believed by some to be spirits or angels of loved ones come to visit. 

Also note that some butterfly's as well as bees, are attracted to some perfumes as well!

According to Native Mythology, the butterfly represents the four stages of development. 
First - the egg 
Second - the larva 
Third - the chrysalis 
Forth - the butterfly. 

If you've got butterflies entering your life, perhaps you should look at your current situation and determine what stage you are at or what stage a particular issue is either in or moving through. That will help you decide what your next, most effective steps should be.