Butterflies are all about metamorphosis and cyclical change. It starts out as a caterpillar, pupates, and then emerges as a gorgeous butterfly. Then it lays eggs and the cycle repeats.
As a result, butterflies also signify forward motion and constant change. In the Cups cards butterflies are about emotional transformation and the colorful, fluttery, dreamy aspects of your subconscious. Think of those hot summer days where the ground shimmers and the only real movement is of butterflies around the flowers.
In Sword cards, butterflies are more about intellectual transformation. In the Modern Witch tarot they appear on the Queen and King of Swords. On the Queen they are on the side of her throne, hemmed in by decoration and the dove right above. She contains the transformation and uses it to set boundaries and make unbiased judgments.
In the King of Swords three butterflies soar above his throne. He is more flexible than the Queen and is a seeker of intellectual truth.