The title of Alice Walker's novel refers especially to one conversation in particular in the book. Though the color purple appears in various places in the novel, it is this conversation that lends a specific meaning to the color as a symbol.
In this conversation Celie and Shug discuss their views relating to God after the two have become involved in a loving relationship.
This conversation marks the true beginning of Celie's self-realization and self-actualization. Shug helps this take place in several ways. One of the ways she helps Celie to mature and to "become herself" is her description of God.
Up to this point, Celie has always pictured God as a light skinned man. Shug tells Celie that she sees God differently. She sees God in everything, including in the color purple. It is the job of humans to recognize the joy and the beauty of creation, according to Shug's perspective. Celie comes to agree with this view.
By extension, purple takes on a rather specific meaning:
The significance of the color purple is that it stands for human hope.
The world, though cruel, is also full of beauty waiting to be recognized.