The screaming noises coming from the nursery at the beginning of "The Veldt" are the eventual screams of George and Lydia Hadley, as imagined by their children Wendy and Peter.
The primary setting in "The Veldt," is the children's nursery, which was constructed by HappyLife Home and was "forty feet across by forty feet long and thirty feet high" and "cost half again as much as the rest of the house." This room is able to tap into the desires of the children and project their imaginings in the room, which is then able to stimulate each of the five senses.
One of the children's imaginings included "a faraway scream" that "sound familiar" within this African veldt, which is filled with lions and giraffes and the like. Later in the story, the narrator reveals who this scream came from: the parents themselves. Right before being eaten by the lions, the narrator says, George and Lydia suddenly "realized why those other screams had sounded familiar.” It's because those screams were their screams.
This wish for death on the Hadleys is foreshadowed early on when the two sit at dinner and George thinks about the death thoughts of his children. He thinks, "Long before you knew what death was you were wishing it on someone else.” So the children, who were angry at their parents for attempting to take away their true caregiver (the house) wish death on their biological parents. This fantasy is played out behind closed doors in the nursery and becomes a reality when Wendy and Peter lock George and Lydia inside.