In this novel, "The Giver," the community is isolated and they have no memories they have not be given. All of the memories are stored in the mind of The Giver. At one time in the long ago past the community found memories of things such as war, death, and fear too hard to bear, so they gave away all their memories to one man.
The reason the jet would frighten the people is because they didn't really understand what the jet was and it might mean that their way of life was being threatened. It is at the beginning of this experience we meet Jonas, the protagonist of this story and the eventual receiver of Memories.
"At any one moment individuals must be prepared to respond to announcements made through the ubiquitous loudspeakers. A day's holiday is proclaimed and everyone takes a rest from work. There is no opportunity for planning an individual vacation. There is nowhere to go, not much else to do. The community can only be successful in curtailing individual freedom by severely limiting the choices available to individuals. Hence, the community is paranoid in its insularity. Hence, the panic at the beginning of the novel, when an unidentified plane flies overhead."
The Lois Lowry young adult novel is written about a utopian society somewhere in the future. This being the case, the reader must think about what previous times in the society would have been like. Think about societies today. Most have been involved in or are aware of warfare, terrorist attacks, and etc. Therefore (although I cannot remember if it is stated specifically in the novel) the sight of fighter jest flying over the community could remind them of previous times when these represented a threat to their safety or way of life.
A very basic answer to this question is fear of the unknown. As others have posted, the residents of this community only know this version of Utopia - though whether or not the community is Utopia is debatable and probably the realm of another discussion. When confronted with something that large, apparently "floating" above you in the sky with no prior knowledge of what it is a very frightening proposition. It is a very similar situation as in most alien invasion movies.