The larger purpose of Pres. Lyndon Johnson's "Great Society" was to use government programs to fix the most pressing problems that faced American society. Pres. Johnson wanted to fix all of these problems so that, in his words, American society would become "great" again.
For example, Johnson wanted to use government programs to improve the standards of education, especially for disadvantaged students (this was the point of the Head Start program as well as much of the point of the Volunteers in Service to America or VISTA program). He wanted to declare a "War on Poverty" that would eradicate that problem as well.
As the name implies, Johnson was trying to eradicate problems in American society and make the society great again through the use of government programs.