One of the most befuddling aspects of UFO stories is how many of them are *so* bizarre. I'm not even talking about the strangeness of humanoid aliens visiting Earth from another planet; that is strange for a lot of reasons already, but UFO encounters take it up several more notches. The classic example is the aliens that landed on a chicken farmer's yard and asked for water in exchange for dry cookies:

One of the men held up a jug apparently made of the same material as the saucer. His motions to Joe Simonton seemed to indicate that he needed water. Simonton took the jug, went inside the house, and filled it. As he returned, he saw that one of the men iviside the saucer was "frying food on a flameless grill of some sort." The interior of the ship was black, "the color of wrought iron." Simonton, who could sec several instrument panels, heard a slow whining sound, similar to the hum of a generator. When he made a motion indicating he was interested in the food that was being prepared, one of the men, who was also dressed in black but with a narrow red trim along the trousers, handed him three cookies, about three inches in diameter and perforated with small holes.

Passport to Magonia by Jacques Vallee

These are the stories that resist any kind of rational explanation. Even the most staunch skeptic could eventually get on board with humanoid extraterrestrial intelligence visiting Earth, there are many books and movies about such events and they're fantastical but possible. But the idea that ET would traverse the galaxy to land on a guy's yard and ask for a jug of water is preposterous. Then the grill and cookies just push you to a level of absurdity that is truly stranger than fiction.

And yet, this story was investigated by the Air Force during Project Blue Book and the veracity of the tale is backed up by renowned UFO researches Jacques Vallee and J. Allen Hynek. Simonton even still had the cookies, which apparently tasted like cardboard.

Grant Cameron came up with a great theory for these stories. He believes they're something that lucid dreamers call "dream signs":

if you want to get lucid in a dream what you got to do is you got to get the dream sign, and the dream sign is [this] weird thing that happens in the dream that you're supposed to pick up [on] that you're dreaming

Grant Cameron - Consciousness & the UFO Enigma: Redefining Reality

As I understand it, if you're trying to learn how to lucid dream you're taught to look for something called "dream signs" which are any irregular phenomena that indicate that you're not in reality. You might see six fingers on your hand, or your dog is driving a car. In spite of their absurdity, the nature of dreaming seems to be that you often don't notice this absurdity until you wake up and remember that dogs can't drive cars.

One common dream sign involves clocks. Lucid dreamers often report something like 37 hours on the face of a clock, or too many hands and some of them moving in the wrong direction. There are several strange UFO stories about clocks and time as well:

When a witness meets a UFO occupant who asks, "What time is it?" and replies, "It's 2:30," only to be bluntly told, "You lie – it is 4 o'clock" (this actually happened in France in 1954), the story is not simply absurd. It has a symbolic meaning beyond the apparent contradiction of the dialogue. Could it be that the true meaning of the dialogue is "time is not what you think it is"?

Dimensions by Jacques Vallee

Among other things ... he noticed a box with a glass top that had the appearance of an "alarm clock." The "clock" had one hand and several marks that would correspond to the 3, 6, 9, and 12 of an ordinary clock. However, although time passed, the hand did not move, and Antonio concluded that it was no clock.

Passport to Magonia by Jacques Vallee

There's really no other category that fits these stories as well. They don't sound like science fiction or fantasy which have some internal logical consistency, and they don't sound like myths which usually have some kind of moral or historical lesson. As Vallee describes it:

It is the poetic quality of such details in many UFO sightings that catches the attention—in spite of the irrational, or obviously absurd, character of the tale—and makes it so similar to a dream.

Passport to Magonia by Jacques Vallee

What do the dream signs in UFO stories mean? They seem to be pointing us to something about our reality that we don't yet understand, that what we currently consider as "real" is in some ways illusory or dreamlike.