Anybody know why they're required to wear them?
Superstition, pure and simple.
Why YES!
You can find the requirements by looking in our Scriptures!
--MormonDude(Wait! No you can't!)
Adult Latter-day Saints who have been to the temple make sacred covenants to follow Christ. There, they receive what is called a "garment" to wear as a personal, private reminder of those covenants. It's related to the Biblical concepts of priestly robes and vestments and "wearing the whole armor of God," with the garment itself representing the garments God gave Adam and Eve in the garden of Eden. There are also other outer articles of clothing worn only in the temple.From lds.org Wearing the temple garmentThe temple garment is modest underclothing. It's not exactly Calvin Klein, but it's not necessarily funny looking, maybe just a little more modest than usual. Promoting modesty is one of the intentions, I think, in addition to remembering covenants of integrity and virtue. Garments
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.And again from lds.orgThe 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.
In The Church of Jesus Christ of Latter-day Saints, garments are worn beneath street clothing as a personal and private reminder of commitments to God. Garments are considered sacred by Church members and are not regarded as a topic for casual conversation.