This is really, really long. Just FYI.
My dh and I have talked about priesthood. I think that ldsapmom has a good description of priesthood.
Dh says that anyone who wants the priesthood for a *power* trip has the wrong idea. The priesthood holder cannot do ANYTHING for himself with the priesthood. In fact, if he humbly feels that he could use a blessing (for support, if he's sick, etc.,) he has to go to a friend, bishop, home teacher, etc. who holds the priesthood and ask him for a blessing.
In the proclamation on the family (released in 1998?) by the First Presidency they state that (paraphrased--I can't find my copy right now) gender is a basic part of our divine nature. Men and women each have characteristics of their spiritual and physical selves that they have to mesh with becoming godlike. A member of our stake presidency in another city described why the priesthood is for men something like this (which I strongly agree with): women have certain inborn physical and spiritual traits, among which are included, greater spirituality, meekness, humility, love for others, etc. Whether it's testosterone or something else, men have competitive natures, are more prone to anger, etc., and therefore having and holding the priesthood provides men the opportunity to increase spirituality, humility, love for others: all characteristics that Christ had, that we are all trying to approach.
Sometimes it seems like non-LDS people think that members of our church accept these doctrines at face value and do not struggle with them, to know they are of God, but speaking for myself, I know that I have struggled with a lot of difficult doctrines and had to pray, study scriptures and the writings of the prophets, and discuss (usually with dh or my dad) with someone to hash out my ideas. As ldsapmom said though, I started with the basic faith that I believed that ______ was the prophet or the scripture, and if that's what it/he said, then I had to resolve it in my mind.
I also want to address the racial issue: In Nauvoo (1830s), Joseph Smith was about to ordain a freed slave, and that was when he received the revelation from God that persons of color were not to receive the priesthood at that time.
In 1978, the First Presidency received the revelation that the priesthood and the blessings thereof were to be available to all God's children, regardless of color/race.
Some people look at this and say, "how convenient, that 'God' said that it is suddenly okay for everyone to receive the priesthood." This is a definite faith type issue. I don't always understand the reason why, but I can share a family story that may point to the Lord's reasoning on this issue.
We believe that revelation comes line upon line, precept upon precept. What that means is that a bit at a time comes, and it meets the followers of God where they're at. Occasionally, a piece of light is even removed because of a lack of faithfulness.
In 1978 my grandfather died. He was from the south, and had strong, very bigoted and biased ideas about race. My dad said that his father had "taught" him some things that were very racist, and my dad could never turn his dad's mind around. If the revelation for the priesthood going to all had been given in, say, 1950, or 1930 (during all the development of eugenics
), there might have been an even greater falling away from the church, with hundreds or thousands of people losing faith because they couldn't align their faith with their social views. My dad said that if it had come before my grandfather died, he would have never have been able to accept it.
1978 seems "convenient", being right at the end of the Civil Rights movement starting in the 1960s, etc. This is where faith comes in: I believe that Spencer W. Kimball who was our prophet at the time was inspired to inquire about the issue, and pray deeply and long, and the Lord let him know that it was time.