While it has one of the coolest sounding names ever, the willing suspension of disbelief is also one of the most important narrative functions. Stories simply wouldn't work without it.
The willing suspension of disbelief describes when readers (or viewer, depending on the given narrative form) allows the story's artificial structures to create a real experience for them. In other words, the reader, in his own mind, accepts that the given story is untrue and is being told through an artificial medium but still believes in it, anyways.
The most obvious example of this in novels is dialgoue. People simply don't talk that way: in complete sentences, without any "Um"s or "Ah"s, and definitely not as witty. Readers ignore this fact and can enjoy the story anyways, given their willing suspension of disbelief.
Another example is stories that simply cannot happen in today's world. The fantasy and science fiction genres take a lot of willing suspension of disbelief, which is why some readers don't enjoy them. It's not that these readers don't have imaginations, but rather that they are unwilling to divorce themselves from reality that much.
The willing suspension of disbelief happens in film, TV, and plays, as well, with the viewer allowing that these things simply don't happen the way the screen or stage shows them to. This could happen through a slow action shot, slight changes of point of view that are inaccurate but provide the prettiest images, or characters who can do superhuman things.
Many psychologists believe that humans are born with this ability, given that sometimes brain damage, psychological disorders, or other trauma to the mind causes an inability to distinguish fact from fiction. Schizophrenics, for example, would have too much willing suspension of disbelief, as they can become paranoid due to beliefs in false stories. Also, humans have told stories for at least as long as recorded history, in forms that would require the willing suspension of disbelief to make them understandable.
Readers understand that to enjoy a story, we must accept that life does not happen in this way but we follow along, anyway, hoping for a good time.