Jonas is apprehensive because he is about to turn twelve. Or at least it is about to be the Ceremony of Twelves for all the kids who are about his age.
At this ceremony, all of the kids who are 12 are going to be told what their job will be for the rest of their lives. In this society, people get assigned to jobs rather than trying to figure out for themselves what they want to be.
Jonas is worried because he has no idea what he wants to be and he has no idea what he would be good at. So he's worried that he won't get picked for anything.
In chapter one of The Giver, Jonas is feeling anxious. At first he thinks he is frightened, but realizes it is apprehension he is feeling. The Ceremony of Twelve is coming up, and this is a big deal for all the kids who are eleven. At this ceremony the kids will find out what their jobs will be, and they will have these jobs until they have to go to the home for the old. Jonas is apprehensive about what job will be chosen for him.
He had waited a long time for this special December. Now that it was almost upon him, he wasn't frightened, but he was...eager, he decided. He was eager for it to come. And he was excited, certainly. All of the Elevens were excited about the event that would be coming soon.
But there was a little shudder of nervousness when he thought about it, about what might happen.
Apprehensive, Jonas decided. That's what I am.
This ceremony is the most important part of a young person's life, and Jonas is well aware of that. Whatever job they will be given at this ceremony, they will have until it is time for them to "retire". Little does Jonas know that the job he gets is going to change his life forever.