They serve as a constant reminder of the unstable nature of their society, the unhappiness that exists within it, and the potential for disaster and tragedy. The jets are there in the background, an ominous warning of the destruction that their society could potentially face. Wars are going on constantly; many of Mildred's friends have husbands who are enlisted in the wars, and it could reach their shores at any time. In a society that practically breeds violence, the fact that war is a part of it is not a surprise.
Bradbury also uses war as a literary technique to enhance suspense, tension and mood. When Montag discovers the bottle of pills that Mildred had overdosed on, "the sky over the house screamed. There was a tremendous ripping sound...Montag was cut in half. He felt his chest chopped down and split apart. The jet bombers...did all the screaming for him." This is symbolic of Montag's own screaming despair at discovering Mildred's attempted suicide. He is upset, realizing how unhappy they both are, and it tears him apart. So Bradbury uses the jet bombers to enhance the mood, and as a symbol for Montag's chaotic emotional state.
The war, which mostly occurs in the background of the story, is meant to show two things; that this society has not solved all of its problems, and that its people don't seem to care.
Much of the exposition we are given, such as that from Beatty, suggests that we are meant to envision this society as a reasonable, if irrational, evolution of our own. This society is primarily concerned with feelings; if people feel good, they are content, and if they feel bad they are discontent. Since discontent leads to problems, it is better for people to feel good, at all costs. However, the fact that this society has participated in wars (Montag even specifies that they started two of them) suggests either that this society is obscenely delusional or has simply insulated itself against its own hypocrisies.
The jets are an immediate and physical reminder of the war, which might otherwise be argued away as a voice on the radio or a picture on a screen. The jets embody the swift, deadly and impersonal side of this society, all the elements that are the result of focusing too much on conformity and efficiency. The jets exist as if to dare observers to ignore them. Montag points this out rhetorically asking "how did they get up there every hour of the day without us noticing?" and indeed, Mildred doesn't seem to notice or care.