What do Nosebleeds in Anime signify?

Often times you will see one of the characters (typically a male character) experience a nosebleed.  This phenomena is associated with sexual excitement.  I don't understand why the Japanese associate this with nosebleeds but there have been some that launch the character into the sky so hard that they disappear with the stereotypical vanishing *ding*.  This has been accepted into the common Anime.  So if you see this occur, you can expect that some undergarment or nudity preceding the event.