The literal meaning of the word "hijaab" ( حجاب ) in Arabic is NOT headscarf. It actually means a barrier or partition. It comes from the verb which means "to form a separation between" and "to cover."
Its interesting how the word is used in the Quran. God says:
وَبَيْنَهُمَا حِجَابٌ ۚ وَعَلَى الْأَعْرَافِ رِجَالٌ يَعْرِفُونَ كُلًّا بِسِيمَاهُمْ ۚ وَنَادَوْا أَصْحَابَ الْجَنَّةِ أَن سَلَامٌ عَلَيْكُمْ ۚ لَمْ يَدْخُلُوهَا وَهُمْ يَطْمَعُونَ
And between them will be a partition, and on [its] elevations are men who will recognize all by their marks. And they call out to the companions of Paradise, "Peace be upon you." They have not [yet] entered by they long intensely. [7:46]
In this verse the "hijaab" is referring to a wall/partition/barrier that is put between the people of Heaven and the people of Hellfire. And on this partition are a group of people whose good deeds are equal to their bad deeds and so they're waiting for their judgement, not knowing which side of the barrier they'll be put on.
What is interesting here is the purpose of this barrier. It clearly and physically separates those who were righteous in this world from those who were not.
Now lets backtrack to the cultural use of the word "hijaab." These days its used to refer to the headscarf which many Muslim women wear to cover. Historically however it is a state which a Muslim man and Muslim woman both observe; a state of modesty and a state of openly identifying as a Muslim. This state is both internal and external. Internally, one's heart is attached to God and thus puts a barrier around it protected one's self from that which will deter him or her from God. Externally, it puts a barrier from oneself from those who are not Muslim. This external barrier is not to shun people, but it is to show and be proud of one's Islamic identity.
The beauty of Islam is that its not actually a religion as we define religion. It is a way of life which encompasses every facet of the believer's life rather than compartmentalizing it like many other religions.
Thus when a Muslim woman specifically chooses to observe hijaab, part of it manifests outwardly in covering her external beauties by covering her hair, breasts, and dressing modestly in a dignified manner.
I've been asked many times by people about my hijaab: "Don't you feel oppressed? Wouldn't it just feel liberated to not have to cover?"
My hijaab is my representation of liberation, a right God has bestowed on all women. We live in a day and age where women are oppressed by men's sexual desires. Women are the objects of sexual entertainment in media all around us. We're oppressed by this media that tells us to be free by taking off our clothes and exposing ourselves the world. My hijaab reminds me that I am of extreme worth and value, that my value is not by my external body but by my internal soul, that to have a sense of dignity is where my freedom lies. So no, I don't feel oppressed. Rather, I feel liberated. I feel free. I feel beautiful. I feel Muslim.