At first glance, this mitzvah would appear to be a prohibition only against cursing a deaf person. It is understood to refer to any person who is metaphorically “deaf” to the curse – that is, anyone who can’t hear it to stand up for himself. In support of this interpretation, we have Exodus 22:27, which tells us not to curse “among your people.” (That verse refers specifically to a leader of the nation. Between that verse and this one, we have commands not to curse the powerful and not to curse the downtrodden. It’s certainly logical that we shouldn’t curse anyone in between those two extremes!)
We may say that words have no power, but there seems to a universal stigma when it comes to curses. Maybe words have power after all. Perhaps we should be careful what we put out there in the atmosphere. Even if words have no inherent power, they generate bad will when it gets back to the injured party that another person wished him ill.
The reason underlying this mitzvah is that God does not want us to harm one another – not physically, not financially, not through gossip and not through curses. Whether curses are effective or not, one can’t deny that such things are harmful to interpersonal relationships!
This mitzvah applies to both men and women in all times and places. It is discussed in the Talmud in tractate Shevuos on pages 35a-b. It is codified in the Shulchan Aruch in Choshen Mishpat 27. This prohibition is #317 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #45 of the 194 negative mitzvos that can be fulfilled today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.