What is the reason and meaning of the symbols on the garments worn by Temple-worthy LDS members?

I mirror Matt's sentiments in that I won't be discussing any specific symbols or rituals that are administered in the temple; they are quite sacred to me, and excessive public discussion on their nature cheapens them in my opinion. I don't mean to offend you if this is an honest inquiry, it's just how I feel on the matter.

However, I can speak somewhat on the origin of the symbols themselves, or rather the unimportance of the same.

I've transcribed an excerpt from an excellent interview of LDS scholar Terryl Givens by the podcast Mormon Stories. (Part four, beginning at around 59:30)

TG: All great religion is plagiarism, especially in the Mormon conception of things because it's not possible to create anything new, right? It was all known to Adam. There's this gospel that we're all trying to reach back and grope toward and reconstitute in its entirety and fullness. So if that's the paradigm you begin with then there's no such thing as novelty and innovation in religious thought, we're just trying to recuperate.

There are other people, like I think Michael Smith is one, who are doing really interesting work on the influence of Masonry in early Mormonism. I certainly don't know the full story, but, you know I'm reminded of a priest that I used to work with who came back from a mass he had just celebrated where he used beer for the wine and potato chips for the wafer. And I remember at the time I thought, that was a little bit over the top and blasphemous... and, you know, to some extent maybe it was, but the point he was trying to make to his congregation was, it doesn't matter what symbols we use. It doesn't matter. And we could rewrite the temple ritual tomorrow and use Boy Scout signs and handshakes and it wouldn't matter. It's so immaterial what are the actual, right, physical aspects of the ritual that we go through in the temple.

Joseph found Masonic ritual adaptable in ways that suited his purposes. He seemed to think that the Masonic ritual was an actual if corrupted inheritance from an ancient endowment. Now, the best scholarship today believes that Masonry is a fairly late invention out of whole cloth in the 17th century, right? I don't know where Masonry comes from, I don't know what its relationship is to an original Adamic endowment, and I don't care. Because I don't go to the temple because I believe that the actual ritual I am engaged in has any inherent value. What has value are the covenants that we make, the promises that we receive and the relationships that are eternalized. And so I just say, well bravo to Joseph Smith for finding a system that was quick and readily adaptable to his purposes.

MS: So, the Masonic stuff, you know the ritual, is sort of like the delivery vehicle for the doctrine and the covenants, is that what you're saying?

TG: Exactly.

(Emphasis mine)

This is in no way authoritative, as Terryl Givens is not in a general leadership role in the LDS Church. However, his opinion on the matter seems true to me. To summarize, the form that the symbols take are not necessarily crucial in their own right. They are a delivery mechanism for the sacred aspects of the Gospel that we partake in in the temple.

I have no problem discussing this, because the promises made in a temple to not reveal certain things do not involve the Garment.

The language used in the Temple to explain the marks is this:

[The mark of the square] is placed in the garment over the right breast, suggesting to the mind exactness and honor in keeping the covenants entered into this day.

[The mark of the compass] is placed in the garment over the left breast, suggesting to the mind an undeviating course leading to eternal life; a constant reminder that desires, appetites, and passions are to be kept within the bounds the Lord has set; and that all truth may be circumscribed into one great whole.

[The navel mark] is placed in the garment over the navel, suggesting to the mind the need of constant nourishment to body and spirit.

[The knee mark] is placed in the right leg of the garment so as to be over the kneecap, suggesting that every knee shall bow and every tongue shall confess that Jesus is the Christ.

Source: http://ldsendowment.org

However, this interpretation of the marks was added by David O. McKay in the late 1920s. There's no documentation (that I'm aware of) that indicates whether this is his personal interpretation or was divinely revealed. Personally, I believe it's the former, because there was a slightly different interpretation that was given in the late 1880s:

According to a description by LDS Church President John Taylor in 1883, the "Square" represents "the justice and fairness of our Heavenly Father, that we will receive all the good that is coming to us or all that we earn, on a square deal", and the "Compasses" represents "the North Star". In addition to the Square and Compasses, Taylor described the other symbols as follows: the collar represented the idea that the Lord's "yoke is easy and [his] burden is light", or the "Crown of the Priesthood"; the double-knotted strings represented "the Trinity" and "the marriage covenant"; the navel mark represents "strength in the navel and marrow in the bones"; and the knee mark represents "that every knee shall bow and every tongue confess that Jesus is the Christ".

Source: http://wikipedia.org

Since these are symbols, their meaning is infinitely deep and subject to personal interpretation. When I think of the Compass and Square, I think of the geometer's tools and God's use of them in designing and constructing the universe. As for the navel and knee marks, I have no idea.