[edit: In the comments of this post there was a good discussion of this section. Commenter Kristen has clearly thought about this passage a lot and has a good detailed section about it on her webpage. Anyone who is interested in this should go check it out]
This section is completely bizarre to me, I'll break it down as best I can, but it seems to me that it is just a cultural relic.
The head of a man is Christ, the head of Christ is God, and the head of a wife is her husband.
I'm going to assume that being the head of someone means they are subordinate to you or something. A good example of sexism in the bible. I'm not sure how God being the head of Christ fits in with the whole trinity thing, although I've never really understood the trinity so I'll move past this. Another interesting thing here is it doesn't mention unmarried women. I suppose unmarried women were thought of as property of their fathers and not worth bringing up.
If a man prays or prophesies with his head covered he is dishonoring Christ, but if a woman prays or prophesies without her head covered, she is dishonoring her husband.
I don't understand why there would be a difference, is a head covering an honor or a dishonor? This is what I mean when I say it must just be some cultural relic.
If a wife will not cover her head, then she should cut her hair short, but this is a disgrace so she should cover her head. A man should not cover his head for he is the image and glory of God.
Woman was made from man but we are all born of women, so women should wear a symbol of authority on their head.
I really don't understand what these things have to do with one another.
If a man wears long hair it is a disgrace, but if a woman has long hair it is her glory.
So why do we cover it up? This whole section makes no sense to me. It seems to me that it is simply reflecting the preferences of the person speaking and/or the style of the time and simply claiming that God wants it that way too.
The Lord's Supper
When you come together as a church to eat the bread and drink the wine, do so properly or you will bring judgement on yourself. You should not have factions in your church. You should not come to church hungry, you should eat at home first.
I understand the idea of not having divisions in the church. That seems like a good thing, cliques are bad and whatnot. I don't really get the part about being hungry. Perhaps it used to be a full blown meal that was done there and people were taking advantage? I don't really know.
Spiritual Gifts (ch 12)
Paul is talking to Pagans, he says that different people have different spiritual gifts, yet they all come from the same spirit. The spiritual gifts include: utterance of wisdom, utterance of knowledge, faith, healing, working miracles, prophecy, the ability to distinguish between spirits, speak in tongues, and interpretation of tongues.
My understanding is that Pagans have a different God for each action that a God might do. In this context, this section makes sense if he is talking to former pagans, he's trying to explain how their old religion was wrong.
One Body with Many Members
Everybody is part of the body of Christ. We all rejoice together or suffer together. It is like one person is the foot, another is an eye, we need each other. Some people seem less important, but God made it that way.
Interesting metaphor I guess, we should help each other out is always a good message.
For the Corinthians Overview Post:
12:25-26 Help each other out
11:3 Women should be subordinate to their husbands