The title of Alice Walker's novel is taken from a line in the text. Shug tells Celie that she thinks it irritates God if people walk past "the color purple in a field somewhere" and don't pause to look at it. What Shug is saying is that the world around us is full of beautiful things—in this case, this is symbolized by purple flowers, which are unusual and particularly delicate, appearing in the midst of a field. Most flowers found growing in the wild are yellow, pink or white; a purple flower is something significant and special, and she believes God has placed these flowers in the world as examples of independence and outstanding beauty.
An independent person, then, should be like a purple flower. Purple has historically been a color associated with royalty; it is a dye that was hard to find and therefore worn only by the wealthy, exactly because purple flowers are not very frequently found. But these flowers do exist, and we should pause to recognize that and appreciate the beauty in the world around us, even when things seem grim.