1Co 14:29-35 NASB - "29 Let two or three prophets speak, and let the others pass judgment. 30 But if a revelation is made to another who is seated, the first one must keep silent. 31 For you can all prophesy one by one, so that all may learn and all may be exhorted; 32 and the spirits of prophets are subject to prophets; 33 for God is not a God of confusion but of peace, as in all the churches of the saints. 34 The women (wives) are to keep silent in the churches; for they are not permitted to speak, but are to subject themselves, just as the Law also says. 35 If they desire to learn anything, let them ask their own husbands at home; for it is improper for a woman (wife) to speak in church."
This is not seen by most commentators to be requiring complete silence since Paul has already stated that women can pray and prophesy as long as they are in proper submission to their husbands and are modest ("the head covered"cultural meaning of proper respect towards authority and modest dress).
1Co 11:5 NASB - "5 But every woman who has her head uncovered while praying or prophesying disgraces her head, for she is one and the same as the woman whose head is shaved. (thought to be a sign of prostitution)"
It is clear that women did prophesy.
Jdg 4:4 NASB - "4 Now Deborah, a prophetess, the wife of Lappidoth, was judging Israel at that time."
2Ki 22:14 NASB - "14 So Hilkiah the priest, Ahikam, Achbor, Shaphan, and Asaiah went to Huldah the prophetess, the wife of Shallum the son of Tikvah, the son of Harhas, keeper of the wardrobe (now she lived in Jerusalem in the Second Quarter); and they spoke to her."
Isa 8:3 NASB - "3 So I approached the prophetess, and she conceived and gave birth to a son. Then the LORD said to me, "Name him Maher-shalal-hash-baz;"
Luk 2:36 NASB - "36 And there was a prophetess, Anna the daughter of Phanuel, of the tribe of Asher. She was advanced in years and had lived with her husband seven years after her marriage,"
Act 2:18 NASB - "18 EVEN ON MY BONDSLAVES, BOTH MEN AND WOMEN, I WILL IN THOSE DAYS POUR FORTH OF MY SPIRIT And they shall prophesy."
Act 21:8-9 NASB - "8 On the next day we left and came to Caesarea, and entering the house of Philip the evangelist, who was one of the seven, we stayed with him. 9 Now this man had four virgin daughters who were prophetesses."
The key here could be that Paul did not want wives (the Greek word for women can be translated wives and in the context they are recommended to speak to their husbands). It appears that Paul did not want wives looking like they were debating their husbands in public. Clearly the early church allowed an open discussion of theology and this lead to unique interaction during the service.
Others believe that the communication that Paul has in mind is the authoritative teaching given by the elders. This Paul has prohibited in other writings (1 Timothy2:12). The “law” here may be the Roman civil law that prohibited women from giving public testimony and Paul may have seen authoritative teaching in this category, since it is not exactly clear where in the law of Moses or the prophets there is such a restriction.
So it would be important for us to understand this passage in context and within the historical/cultural realities of the time.