The title refers to the desire of the central character, an African American girl named Pecola Breedlove, to have the bluest eyes in the world. Of course blue eyes commonly occur in Caucasians rather than people of African descent, and many examples are given in the novel of the African American characters admiring physical characteristics associated with Caucasians. These include the Shirley Temple cup (with white skin and blue eyes) owned by one of her friends (Pecola is scolded for drinking so much milk at their house--in truth she just wants to use the cup), the white, blonde dolls given to the girls, and the favoritism (even among children on the playground) granted to a light-skinned African American girl named Maureen while Pecola is constantly told she is ugly because she has dark skin (essentially because she looks African rather than European).
The very unhappy life of Pecola (her father is an alcoholic who eventually rapes her) is contrasted with the happy lives of white characters in the movies (her mother Pauline idolizes Jean Harlow) and in children's books. Eventually she becomes mad as the only way to escape from this world. But it is not only Pecola's particular misfortunes which doom her; she also subscribes to the false values of her community which make her unable to value herself and her own individual characteristics. She wishes to have blue eyes to see her world in a new light, a wish which cannot literally be granted, and she is unable to accomplish the necessary mental adjustments to see the world differently (granted she is a child and is adopting the values of her community).
But Pecola's acceptance of the community's standards of beauty is contrasted with that of Claudia, the novel's narrator, who dislikes Shirley Temple and dismantles a white doll she is given for Christmas.