Wearing the Temple Garment
Once people are endowed, they have the blessing of wearing the temple garment throughout their lives. They are obligated to wear it according to the instructions given in the endowment. Those who have been endowed in the temple must remember that the blessings that are related to this sacred privilege depend on their worthiness and their faithfulness in keeping temple covenants.
The garment provides a constant reminder of the covenants made in the temple. The garment should be treated with respect at all times. It should not be exposed to the view of those who do not understand its significance, and it should not be adjusted to accommodate different styles of clothing. When worn properly, the garment provides protection against temptation and evil. Wearing the garment is an outward expression of an inward commitment to follow the Savior.
From WIkipedia [as of 4/28/15]
A temple garment (also referred to as garments, the garment of the holy priesthood, or Mormon underwear) is a type of underwear worn by adherents of the Latter Day Saint movement after they have taken part in the endowment ceremony. Garments are worn both day and night and are required for any adult who previously participated in the endowment ceremony to enter a temple. The undergarments are viewed as a symbolic reminder of the covenants made in temple ceremonies and are seen as either a symbolic or literal source of protection from the evils of the world.
The garment is given as part of the washing and anointing portion of the endowment. Today, the temple garment is worn primarily by members of The Church of Jesus Christ of Latter-day Saints (LDS Church) and by members of some Mormon fundamentalist churches. Adherents consider them to be sacred and not suitable for public display. Anti-Mormon activists have occasionally publicly displayed or defaced temple garments to advance their opposition to the LDS Church.
Temple garments are sometimes derided as "magic underwear" by non-Mormons, but Mormons view this terminology to be both misleading and offensive.
Photo from wikipedia on the modern garments:
The Church officially announced that garments should be worn when doing yard work. Reference: Dec 9, 2011 First Presidency Letter
Critic's comment: This seems to many people, especially those living in hot climates, to be a totally unnecessary burden. What purpose is served by people getting unnecessarily hot and sweaty when working in their own yard on a hot afternoon in Florida?
It's interesting to note that many LDS have said similar comments about Muslim women being dressed head to toe in black burqas in unbearably hot weather.
Does the Lord really care so much about what underwear people wear when doing yard work?
"Temple Garments," from the Topics section of Newsroom, the official public relations arm of the LDS Church. It includes a video dipicting the garments.
Ensign article (Aug 1997): The Temple Garment: “An Outward Expression of an Inward Commitment”
MormonThink Temple - Garments section
Evolution of the Temple Garment: ReThinking Mormonism-garments
Wikipedia on the Garments