What are mormon garments and why do they wear them?

Great question. I'll do my best to answer you're question briefly. To start, I will mention that my dad is Jewish, I have a great friend that was jewish who converted to the Church of Jesus Christ of Latter-Day Saints, and I myself am I convert to the Church (though I was not Jewish) and have studied Hebrew.
The wearing of symbolic garments has been a practice in Jewish culture for a very long time. Orthodox Jews today still wear "tzit tzit" (pronounced tseet tseet). These are frays or tassels that are attached to a tallit gadol, which is a garment Jews wear that have tzit tzit on the corners (Numbers 15:38, Deuteronomy 22:12).
Now here is the commandment God gave to Israel, the covenant people:
"Speak unto the children of Israel, and bid them that they make them fringes in the borders of their GARMENTS throughout their generations, and that they put upon the fringe of the borders a ribband of blue:
‘And it shall be unto you for a fringe, that ye may look upon it, and REMEMBER all the commandments of the LORD, and do them; and that ye seek not after your own heart and your own eyes, after which ye use to go a whoring:
‘That ye may remember, and do all my commandments, and be holy unto your God.” –Numbers 15:38-40
Wearing of the garments serves as a reminder to faithful Latter-Day Saints to keep the commandments and promises they make to God.
Wearing of these garments was a commandment, and wearing/seeing them was a reminder to do the commandments (or mitzvot).
We know that Jesus was perfect and kept ALL of the commandments. We just read that wearing these garments was a commandment. *So to those of you who mocked the garments are mocking a commandment that the Lord gave AND kept.
Nowhere in the New Testament, is this commandment revoked, but to the contrary, it is reinforced (See Matt 22:11-12, Rev 7:9, 13-14 –referred to as robes, also called raiment). The garments are sacred and symbolic, and not magical in and of themselves. Blessings are given to those who keep the commandments, follow the savior, and keep their garments spotless (spiritually). Again, they are not to be treated lightly.
As for those who commented on Masons, you should know that the masons copied the temple ceremonies from the temple of Solomon.
The temple ceremonies were practiced in ancient Israel by commandment. Yes Joseph Smith was a mason. He corrected (by inspiration) their corrupted form of the temple rites. Again, if anyone mocks them, they are mocking the Lord.
Washings and anointings took place at the ancient temple also (Exodus 29:4-7). Anointing with oil was still in effect after Christ’s resurrection (Matt. 6:17, James 5:14). Also, Christ MEANS anointed one. The Lord restored these sacred things in their purity today

Best Wishes,
Rusty