Traditionally, butterflies symbolize transformation, but they can also have other meanings including acceptance and faith, and butterfly tattoos can represent all of these meanings. The insect gets these meanings from its process of metamorphosis from a caterpillar to a butterfly.
Butterflies go through significant physical changes during their life cycles, and that is where the transformation elements comes in. Acceptance and faith are associated with the butterfly because the insect does not question or try to fight against its metamorphosis. It simply accepts that this is what must happen and gets the reward of being a beautiful flying insect at the end. Tattoo meanings are often very personal and may not always follow the traditional symbolism.