I'll try not to ramble on but as a woman, a Muslim and a feminist it might be difficult lol.
The main significance of the veil/hijab is that it is a requirement of Islam outlined in the Quran.
There is a fairly common misconception that Muslim women wear the viel because Muslim men make them do so. The truth is that this is quite rare. Most women wear hijab because of their faith not because of their men. I know several women who wear hijab against the wishes of their fathers and husbands and my husband has been known to whinge that I look like a granny when I'm feeling a bit lazy and just chuck and abaya (big dress) on rather than getting dressed up.
Hijab/covering also has a fairly feminist dimension in that it explicitly rejects the male gaze.
I'm being lazy now and quoting wikipedia rather than doing my own typing..
Male gaze in relation to feminist theory presents asymmetrical gaze as a means of exhibiting an unequal power relationship; that is, the male imposes an unwanted gaze upon the female. While some argue that women who fit the ideal of female beauty enjoy this gaze, many second-wave feminists would argue whether these women are actually willing, noting that they may be merely seeking to conform to the hegemonic norms constructed to the benefit of male interests that further underline the power of the male gaze.
. By covering muslim women refuse to participate in becoming objects for a male gaze and force interaction that is based upon mental engagement rather than physical appearance.
The irony of course is that in the cultural interaction between Islam and the west the feminist dimension of hijab is generally marginalised and is viewed in the opposite light; as a symbol of oppresion rather than liberation.
Sadly in some cultures with Muslim majorities this is the case but this is more a result of cultural traditions than Islam.
I think one of the sad ironies of our time is the miscommunication between Western feminists and Muslim women. Arguably many Western feminists have followed a fairly rascist agenda that assumes that non-Western women want to be the same as Western women but I think it's true to say that most modern feminists are aware that differant women have different ideals and that we should be striving to help women attain thier own goals rather than imposing ours upon them. That said many of the goals of Western feminists such as sexual equality, women's only space, recognition for the value women's work in the home are made explicit in Islam. Under Islamic law a woman can ask for a divorce if she is not satisfied sexually (The Quran mandates foreplay), upon divorce a woman has a right to a divorce settlement and a marraige isn't considered valid without a pre-nup. These guidelines were laid down over 1500 years ago which is fairly remarkable in light of the fact that until only a century ago women in many Western countries forfieted all their property on their marriage and could not get it back if they divorced. In addition I should mention that one of the best known sayings in Islam is that paradise is at the feet of the mothers. Of course some men have chosen to ignore all these laws and others regarding to women and gender relations.

In regards to proscriptions upon men, firstly there is a law which commands them to lower their gaze. so even if a woman chooses not to observe hijab they should just look away. I went to the Rocks on a friday night once with DH and a very religious friend of his. The poor guy spent the whole night watching his toes lol. In terms of men's dress men are required at the most basic level to cover from their navel to their knees in front of men and women but usually in tradition Muslim societies men's dress is as modest as women's.

That's the short version lol.
If you don't understand my ramblings or have any more questions feel free to ask.