What is the reason and meaning of the symbols on the garments worn by Temple-worthy LDS members? I understand that the sacred garments worn by temple-worthy LDS members include symbols of 1) the square, 2) the compass, and 3) the navel mark, and 4) the knee mark.  I know that some of the symbols are also prominent in Freemasonry and that Joseph Smith had become a Mason early on, so perhaps the meaning of the symbols are similar.

Regardless, my question is why were these particular symbols chosen to be incorporated in the sacred garments and not anything else?  What do these particular symbols mean and is there any significance to the locations where they appear?
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 &quot;Square&quot; represents &quot;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&quot;, and the &quot;Compasses&quot; represents &quot;the North Star&quot;. In addition to the Square and Compasses, Taylor described the other symbols as follows: the collar represented the idea that the Lord's &quot;yoke is easy and [his] burden is light&quot;, or the &quot;Crown of the Priesthood&quot;; the double-knotted strings represented &quot;the Trinity&quot; and &quot;the marriage covenant&quot;; the navel mark represents &quot;strength in the navel and marrow in the bones&quot;; and the knee mark represents &quot;that every knee shall bow and every tongue confess that Jesus is the Christ&quot;.

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.