This is the time of day when
legend has it that one can
make a wish, and there is a greater chance of it coming true.
Though history is vague, it is clear that this myth originated from another one - that of wishing on a star. That, combined with the fact the the number one is the only one that ever fills all four spaces on a 12 hour digital clock simultaniously led to this rather unusual belief.
Some people, like John Victor Ramses, author of 11:11 The Search for the Doorway: A Story of One Man's Quest for Wisdom, perhaps take the whole thing a bit far, though. Many self-proclaimed spiritualists take the concept to something of an extreme:
http://www.angelscribe.com/1111.html
But it certainly can't hurt to make a wish.