What does this verse mean? Well, let's consider it.
First, the previous verse says, "Let your women keep silence in the churches: for it is not permitted unto them to speak; but they are commanded to be under obedience, as also saith the law." We see a crucial thing here: Paul points to the law when he mentions the command for women to be under obedience. He must be pointing to Genesis 3:16 when God told Eve that her desire would be to her husband and he would rule over her. Thus we notice that this isn't a cultural thing, but rather applies to all situations in all times.
Being under obedience is apparently tied to being submissive to the husband, having the husband be the head, etc. Paul applies this structure to the church as well. In the church, apparently the men are also to lead. We find this to be perfectly in agreement with the fact that the two church offices are restricted to men. Thus we see NT scripture painting us a picture of church order.
Now, keeping silence in the churches, not being permitted to speak in the churches, is tied in with this principle. Thus, I think what Paul is referring to is women taking over the leadership roles in churches, and he is forbidding it based on God's order of things. This well accords with what he wrote to Timothy when he said, "I suffer not a woman to teach, not to usurp authority over the man, but to be in silence." The silence the woman is commanded to be in refers to the leadership positions.
Now, we look at the verse of the OP and see that Paul is doing this: placing the woman under the authority of her husband. This is well in keeping with the order of things already laid out.
Now, these verses refer to the leadership positions in the church, and only to those things. Paul is not forbidding women to speak at all in the church setting, but rather is forbidding them from taking the authorative leadership positions. But, let me run this the other way, because that is exactly what Paul does when speaking of marriage and the duties of husband and wife. Paul is placing the leadership roles in the church on the man. So, we see that the men must step forward and take these positions and provide good leadership for the church. If the woman is to learn from her husband, her husband better apply himself and be a sufficient leader. If the woman is not to teach or usurp authority over the man, the man needs to step up and be the leader and teacher the church needs. Men, this responsibility falls on us and we need to step up and fill the role.
This is not, I repeat not, forbidding women from being involved in church affairs. Members of the church have a say in church matters. This is about leadership, and the men are ordained of God to be leaders. We better take that seriously. I know of a church where it is complained by certain others that a female member basically runs the church, and it is suggested that she is overstepping her bounds. Well, that might be right, but I'd rather place the blame where it really belongs and that is on the male members. If they would step up and lead as they should, there wouldn't be a problem.
