Butterflies, due to the nature of their life cycle. . .egg, caterpillar, cocoon, re-emergence as the winged creature are often thought to represent the human cycle of life.  The butterfly is often though to represent eternal life or life in heaven when seen at a funeral; the connection is that as the caterpillar goes into a cocoon and is almost in a death-like state, it re-emerges as a beautiful winged creature, in a "new" life later.