I used to think that "helpmeet" was an archaic noun meaning something like "helper". But these are two separate words translated from the Hebrew "neged" and "ezer" in Genesis 2:18. Ezer means a help or helper. Neged is in the KJV translated into meet, an archaic word meaning something like suitable. But the Hebrew , "neged", is much more multi-faceted than that. It can mean "in front of", "in sight of" or "opposite to". This is what is conspicuous, what you have right in front of you and are facing. But a more implicit and perhaps symbolic meaning is "counterpart".
Here is what is written in Genesis 2:18
And the Lord God said, It is not good that the man should be ; I will make him help meet for him
"The man" in the Hebrew text is Adam. It can be interpreted as a personal name or a noun meaning "man" or "mankind". We see both interpretations in the English translations of the first chapters of Genesis. Eve means "life" or "living". It was not good for man to be alone and so God made him a counterpart, life. I see different levels of symbolism here. Man and woman fit together like two pieces of a puzzle, being incomplete on their own and fulfilling each other. Perhaps a more subtle meaning is this: In Genesis 2:7 man becomes a living soul. In the Hebrew text, Adam becomes a chayah soul. Chavah, which is spelled Eve in English, is a derivative from chayah. So this is a similar concept to Adam getting Eve/life as help meet for him later on. (There are numerous wordplays in the first few chapters of Genesis). Mankind and life go together like man and woman. The existence of mankind is meaningless without the life on earth/mortal experience and possibilities for eternal life.
As mentioned before on this blog, the creation account is full of opposites like heaven and earth, light and darkness, water and dry land, etc. Adam and Eve is the culmination of that account. I sense this understanding in the words of Book of Mormon prophets also. Here is one example
the Lord spake unto him again, saying that it was not meet for him, Lehi, that he should take his family into the wilderness alone; but that his sons should take to , that they might raise up unto the Lord in the land of promise. (1 Nephi 7:1)
The idea that the Lord said it was not good to be alone is a reflection of Genesis 2:18. Just like man needed woman to have life, Lehi's sons needed wives to have offspring. Not only that, they needed to raise up seed unto the Lord. This is the seed that can prosper and grow into life. The Book of Mormon is full of references to the life and prosperity that comes with keeping the Lord's commandments and the death that follows covenant rebellion.
Interestingly, the idea of opposites also frequently show up together with references to Adam and Eve in the Book of Mormon. At least, the passages where opposites are discussed are also those with the most extensive references to the creation and the story of Adam and Eve. The obvious Book of Mormon chapter that comes to mind when speaking of opposites, is 2 Nephi 2, with its famous "it must needs be, that there is an opposition in all things" (2 Nephi 2:11). In the verses that follow, Lehi discusses the creation, heaven and earth, the tree of life and tree of knowledge, and Adam and Eve.
Another Book of Mormon chapter that is full of opposites but perhaps less known for it, is Alma 42. This is, after all, a beautiful discourse on justice and mercy, as masculine and feminine counterparts:
For behold, justice exerciseth all his demands, and also claimeth all which is her own; and thus, none but the truly penitent are saved. (Alma 42:24)
Another example:
Now, repentance could not come unto men except there were a punishment, which also was eternal as the life of the soul should be, affixed opposite to the plan of happiness, which was as eternal also as the life of the soul. (Alma 42:16)
Another one (this one is beautiful):
And thus we see that all mankind were fallen, and they were in the grasp of justice; yea, the justice of God, which consigned them forever to be cut off from his presence. (Alma 42:14)
...and mercy claimeth the penitent, and mercy cometh because of the atonement; and the atonement bringeth to pass the resurrection of the dead; and the resurrection of the dead bringeth back men into the presence of God (Alma 42:23)
This also happens to be the chapter in the Book of Mormon with possibly the most direct and extensive references to Adam and Eve. Similar to 2 Nephi 2, it discusses the two trees, what happened in the garden and the consequences of it.
In light of all this, and hopefully without getting too political, I find it sad that there are strong forces in the modern western world that try to rid society of gender differences altogether. I am all for women's rights and equal opportunities, but I think we lose something valuable when we try to make women more like men or erase the concept of sex/gender altogether. There is beauty in the counterparts. Not only that, but they are the essence of creation and a necessary ingredient in the plan of salvation. Without it, "all things" would just be "a compound in one" and "created for a thing of naught" (2 Nephi 2:11-12)