Paul discusses a sort of "spiritual economy" in verses 3-12, beginning by stating that Christ is the head of every man, and that God (the Father) is the head of Christ. God the Father and God the Son (and God the Spirit) are in essence one—there is one God; still, within the Trinity there's an economy of authority; the Son submitting to the Father and the Spirit to both the Father and the Son. Neither is "less God" than another: it's just the way He "works." So likewise men and women function as part of an economy: men are not "more" than women just as women are not more than men. That said, there's a created order to observe.
How do I handle my family? Am I an effective spiritual leader? Am I seeking God's glory in how I handle family matters? In what areas have I dropped the ball? What do I need to change in order to pick it back up?
"Be imitators of me, just as I also am of Christ."
—1 Cor 11:1
The rest of the chapter focuses on the Lord's Supper (communion) and how some within the church were, in effect, acting as though they were at a party rather than observing the ordinance as Christ delivered it (vv23-26).
I don't think I always take to heart the admonition: "Therefore, whoever eats the bread or drinks the cup of the Lord in an unworthy manner, shall be guilty of the body and the blood of the Lord." It's amazing how one tiny piece of cracker and one small cup of grape juice can—should—invite one to assess the current state of his walk.
What am I saying when I observe communion? Am I really examining my heart, my state before God? Or am I willfully eating and drinking judgment to myself? It's easy to write down "I'm thankful when God disciplines me," (v32), but it's another to really mean it when it happens. And God's discipline—for me, at least—is a hard thing to understand. How is He going to do it? When? How am I to know what's His discipline and what's just one of the consequences of living in a cursed world?