Does one being "born of water" mentioned in John 3:5 mean one being born of a woman? And does this mean naturally occurring? What I'm getting at here is trying to find a direct definition of "being born of water." At first I thought it meant "one being baptized" but I know this isn't so as I believe that to be a symbolism of one's commitment to the Father and not absolutely necessary for salvation.
This question can be answered briefly, but I see that there are underlying concerns involving bapism and salvation. Therefore we will expand the response to include these.
John 3:5, the source of the question, reads as follows:
 Jesus answered, Truly, truly, I say to you, unless one is begotten of water and the Spirit, he cannot enter the kingdom of God.No, it means "begotten of flesh." The context indicates that Nicodemus assumed that was its meaning and Jesus, accepting, did not correct him. In verse 6, Jesus characterized the two begettings as of the "flesh" and of the "spirit." So the contrast in v. 5, of "water" and "spirit" is the same, in which of flesh = of water. The expressions "begotten of woman" or "born of woman" do not appear here.
I affirm what you now believe. Baptism has symbolic significance only and is not essential to salvation. Further than that, it is an act of obedience to the Lord, who commanded us to baptize, and therefore to be baptized. There are some Christian denominations that teach baptism is essential to salvation, as you first believed, but being born of water has no reference to baptism. The context makes this clear and certain. Of water = of flesh.
Yes, this being begotten of the flesh also means naturally occurring. If your concern here is with the modern experimentation with articifial insemination and cloning, such infants are also "begotten of the flesh" aren't they? I do not see here a justifiable distinction.
Jesus made baptism symbolic when he said to John the Baptist, who was about to baptize him:
 Then Jesus came from Galilee to the Jordan to John, to be baptized by him.
 John would have prevented him, saying, "I need to be baptized by you, and do you come to me?"
 But Jesus answered him, Let it be so now; for thus it is fitting for us to fulfil all righteousness. Then he consented.
The expression translated for thus (Greek, houtos.gar) indicates in such a manner as this, not in this manner. Thus, the symbolism is to death to this world and resurrection to spiritual life in Jesus through imbibing his Word, which is equivalent to being begotten from above in John 3:3. It may, additionally, also symbolize that resurrection from the dead to life in the eternal Glory on the Last Day. By participating in this glorious event, one finally and fully fulfills all righteousness! But the distinction is not significant, since the first (being begotten from above) is requisite for the second. Fulfilling all righteousness does not require that one be baptized in water, but that one have spiritual experience that follows the same pattern, or is like that.
Some commentators (and most translations), seeking to avoid the thought that it is by baptism in water that one fulfills all righteousness, have attempted to make the for thus refer to the fact, as indicated by John's objection, that one must humble oneself (as Jesus was humbling himself by submitting to baptism by one lesser in status than himself) so as to fulfill all righteousness. This is unlikely since, in context, the entire focus of the event was on the act of baptism, not on Jesus' act of humbling himself.
It seems clear, also, that there is yet another lesson to be drawn from the baptism of Jesus. This is to note that the lesser person is qualified to baptize one greater in status, otherwise Jesus would not have submitted to John's baptism. John was only a servant of God, whereas Jesus is the Son. This contradicts the general impression that one gets, in Christendom and among the churchmen, that one requires a greater than oneself (i.e., one of higher status in the church and before God, ordained and especially qualified to perform such rituals) to perform one's baptism. No, the qualifications of the individual doing the baptizing is not significant; the qualification of the one being baptized is all important.
Baptizing an unqualified person -- that is, one who has not been begotten of the Spirit through the reception of the Word of Jesus -- be it infant or reprobate, only has one significant effect: it makes one very wet!
Let us go back to the context of John 3:5 again, because there is another thing there that is very important. Here are the relevant verses:
John.3The Greek term, anothen, in this translation is critical to understanding this utterance. To realize its exact significance, look at the following verse where the same term appears and where the translation is "above." Jesus answered him, Truly, truly, I say to you, unless one is begotten from above (anothen), he cannot see the kingdom of God."
 Nicode'mus said to him, "How can a man be begotten when he is old? Can he enter a second time into his mother's womb and be begotten?"
 Jesus answered, "Truly, truly, I say to you, unless one is begotten of water and the Spirit, he cannot enter the kingdom of God.
 That which is begotten of the flesh is flesh, and that which is begotten of the Spirit is spirit.
 Do not marvel that I said to you, "You must be begotten from above (anothen).
So, Jesus was informing Nicodemus in John 3:3,7 not that he must be born from above, or again, but that he must be begotten from above. Being himself from above, and making this characteristic of himself a clear specification elsewhere, Jesus was unique in not requiring a new from above birth.
(ek ton.ano); you are of this world, I am not of this world.
The Greek is different, but it means exactly the same thing -- from above. It was doubtlessly stated in this form here so as to make a poetic contrast with ek ton.kato (from below).
To get a confirmation of this, we need only recall that John the Baptist directly made this same categorical distinction between himself and Jesus:
John.3Jesus, being from above, did not categorize himself among those begotten of the flesh or of the earth or from below. So he was not equating or comparing himself with John. He did consider himself to be a man, but a man who, having come from above, did not require a begetting from above. When we have been begotten from above, we enter into the same category as Jesus, who was from above. We become children of God.
 He (Jesus) who comes from above (anothen) is above all; he (John) who is of the earth belongs to the earth, and of the earth he speaks; he who comes from heaven is above all.
Looking back at the history of the church, one who understands these things cannot but be powerfully impressed with the perfidity of the churchmen from a very early time. Convincing the adherents of the faith that baptism was essential to salvation, it then became necessary for each infant to be baptized quickly lest it die unbaptized and go to perdition. Of course, it must also be performed by a properly qualified person, a priest with full credentials from the institution. The child, when grown, never knew a time when it was not a "Christian." Instead, it finds itself an integral part of the system and fully supportive of the ministry that has done such a wonderful thing for one. It is inevitable, then, that one commits one's own children to the same process, and so it goes, century after century. The public is assured of eternal salvation, the priest is assured of a comfortable and respected place in society, and the institutional church is assured of a continuing supply of victims from generation to generation. Real sweet, huhhh?