What is the "nightmare" that now descends upon the children?

The nightmare unfolding around the children’s safe and innocent life is the racism the children will face throughout the arrest and trial of Tom Robinson.  Scout and Jem first confront the racism of the town when they follow Atticus to the jail.  Atticus’ intention is to protect Tom from a lynch mob, and when the children arrive at the jailhouse, the mob is threatening and angry.  Scout, in her innocence, points out Mr. Cunningham in the mob.  Mr. Cunningham represents the racism present in the average Maycomb resident, and this scene allows Jem and Scout to see that this hatred is predominant in people they know and the everyday events of Maycomb.  

Throughout the rest of the novel, Scout learns about hypocrisy through the teachings of her teacher about Hitler’s discrimination of Jews and the outlandish hypocrisy of the missionary circle raising money for a tribe in Africa but who won’t help their neighboring black community.  She also learns about Dolphus Raymond and the discrimination he must endure to live the way he wants.  Jem and Scout are also harassed by their classmates at school for Atticus defending Tom.  Even Mrs. Dubose yells at the children and calls their father a derogatory name. 

The children are living in a nightmare because they are being ostracized and bullied by their friends and acquaintances.  They are no longer living the dream-like state of children but are living the reality of how racism can affect them and those around them.