This question could refer to any number of things. April Hall is the story's protagonist, and readers find out early on that she is afraid of several things that kids her age of are afraid of. April is the new girl in the neighborhood, and she is afraid of having to go to a new school and make new friends. She worries that she will not fit in and that other kids will not like her. She is so scared of all of this that readers are told that April is having nightmares about it:

April was worried because she knew from experience—lots of it—that it isn't easy to face a new class or a new school. She didn't admit it, not even to Melanie, but she was having nightmares about the first day of school.

April is also scared of being abandoned. Sure, April has a loving grandmother who is taking care of her, but April is there in the first place because her mom is off trying to be glamorous in Hollywood. April fears that her mother will completely forget about her.

All of the girls in the story (and even the boys) are afraid of the killer that is loose in the neighborhood. They are afraid of winding up dead like the other little girl. The kids are actually forced to stay inside for long periods of time and not engage in the Egypt game because of the murderer. They suspect that it is the Professor because they have been scared and nervous about him for quite some time; however, the Professor ends up not being the killer.