It seems that the semi-Masonic emblems represent different Mormon mysteries, including the Melchizedek priesthood and the Aaronic priesthood. All these mysteries stem from the imagination of the inventor of Mormonism, Joseph Smith.
First here is a video about the secret underwear, by an amusing Australian who interviews some ex Mormons who explain the magic of the garments and succeeds in buying some (illicitly).
The Mormonism Research Ministry's page The Protective Garments of the Holy Priesthood says
“The garment provides a constant reminder of the covenants you have made in the temple. You should treat it with respect at all times. You should not expose it to the view of those who do not understand its significance, and you should not adjust it to accommodate different styles of clothing. When you wear it properly, it provides protection against temptation and evil. Wearing the garment is an outward expression of an inward commitment to follow the Savior”.
This is a former Mormon, Ed Decker describes a bit about the mysteries of the Mormon religion in this video (part 1 of 2)
Having seen a little bit about this subject, what would you think of America if it elected a Republican president who wears this magic underwear? With this in mind, I think it could be argued that Mitt Romney is the most sane of the Republican candidates. I think that gives Obama a good chance of a second term.
That is not to say that the Mormon couple that I know are not very nice people. The strange thing is, I can imagine that one of them does wear the magic underwear but perhaps not the other.