The Irish myths tend to be recorded as three cycles: The Mythological Cycle or the Invasions, The Ultonian/Ulster/Conorian Cycle, and the Ossianic or Fenian Cycle. (This according to T. W. Rolleston's Myth and Legends of the Celtic Race.) The Invasions is predominantly about the Tuatha de Danaan (pronounced "Tua d'Danaan," as close as I can recall), who are functionally gods that invaded Ireland and claimed it from its previous residents, a race of monsters called Fomorians (pronounced "Fuhvoruh," again, as close as I can recall). The Danaans rule Ireland until the upstart Milesians show up. The Milesians are probably human with some god-like ancestors in their past (they're reportedly from Spain, which also translates in context to the "Land of the Dead"). There is a great battle, during which the Milesians win. But the Danaans don't leave Ireland. According to Rolleston, "By their magic art, they cast over themselves a veil of invisibility, which they can put on or off as they choose." The other translation of this that we talked about in the Ireland trip (which I can't find in the Rolleston at the moment) is that the gods, effectively, go "underground," making their homes in the mounds and cairns, and other such places that later become known as fairy hills.
This is the first clue. Remember that fairy tales and folklore are lumped together with old wives tales and superstitions? What was once a "religion," a true mythology in the Dewey Decimal sense, has had to go underground, into hiding, as the power shifts. (True, the Danaans are still active all through the Ulster Cycle, though they're no longer the heroes. By the time the third cycle rolls around, though, there are fairy kings, journeys into the Land of Youth, and all the trapping (such as rescuing princesses from Monsters) that we see in the continental Grimm stories. The people in power know that the Danaans have been conquered; the "folk," the people of the country--possibly the undereducated, but certainly more traditional--continue to tell the stories. Ritual might not get explained to children (as it may have to be kept secret from the local priest), and the stories might no longer have context as the years go. The stories have to change and adapt to survive.
Why is that important? I suppose it depends on why myth itself is important. If, as Tolkien says, myth is related to truth, then it's possible that just as much (possibly more) truth is handed down in the folk versions of old stories than the recorded versions censored by the groups in power. Or, it could be that the distance between fairy tales and the "original" myths is too great for comparison, and the "truth" is lost in the changes.
As a note, I'm considering asking guest bloggers to write short (one-page max) pieces on what makes mythology or the study thereof important in a modern era. Would that be of interest to people besides me (because I'd be fascinated...)?