The majority of Muslim women who choose to cover, whether it is with a Hijab, Jilbab, Niqab or Burqa, do so out of their own personal choice.  Yes, there are cases of some women being forced to cover, but this is condemned by the majority of Muslims, as there should be no compulsion in Islam.

Muslims look to the Qur’an (and Hadiths) to guide them in how to lead their lives, using the Qur’an we can understand why Muslim women choose to cover.

Tell the believing men to lower their gaze and be modest. That is purer for them. Lo! Allah is aware of what they do. (30) And tell the believing women to lower their gaze and be modest, and to display of their adornment only that which is apparent, and to draw their veils over their bosoms, and not to reveal their adornment save to their own husbands or fathers or husbands' fathers, or their sons or their husbands' sons, or their brothers or their brothers' sons or sisters' sons, or their women, or their slaves, or male attendants who lack vigour, or children who know naught of women's nakedness. And let them not stamp their feet so as to reveal what they hide of their adornment. And turn unto Allah together, O believers, in order that ye may succeed. (31) (Qur’an 24: 30-31)

We can also see that, according to the Hadiths, the Prophet Muhammad (P.B.U.H) advises women over the age of puberty to cover themselves. 

Narrated Aisha, Ummul Mu'minin: "Asma bint Abu Bakr, entered upon the Apostle of Allah while she was wearing thin clothes. The Apostle of Allah turned his attention from her. He said: O Asma', when a woman reaches the age of menstruation, it does not suit her that she displays her parts of body except this and this, and he pointed to her face and hands." Sunnan Abu Dawud 32:4092.

It is because of this Hadith and the Ayah that Muslim women decide to cover.  How they cover themselves depends on knowing what each of these terms mean.

Hijab and Jilbab - According to the Encyclopedia of Islam and the Muslim World, the meaning of Hijab has evolved over time:
The term Hijab or veil is not used in the Qur'an to refer to an article of clothing for women or men.  Rather it refers to a spatial curtain that divides or provides privacy. The Qur'an instructs the male believers (Muslims) to talk to wives of Muhammad (P.B.U.H) behind a Hijab. This Hijab was the responsibility of the men and not the wives of Muhammad (P.B.U.H). However, in later Muslim societies this instruction, specific to the wives of Muhammad, was generalized, leading to the segregation of the Muslim men and women. The modesty in Qur'an concerns both men's and women's gaze, gait, garments, and genitalia. The clothing for women involves khumur over the necklines and Jilbab (cloaks) in public so that they may be identified and not harmed. Guidelines for covering of the entire body, except for the hands, the feet and the face, are found in texts of fiqh and Hadith that are developed later. (Encyclopaedia of Islam and the Muslim World (2003), p.721, New York: Macmillan Reference USA)

Niqab and Burqa - According to the hadith’s the Prophet Muhammad’s (P.B.U.H) wives used to cover their faces so that they would not be to be easily identified or singled out by unwanted attention.

Narrated Aisha: The riders used to pass by us when we were with the Messenger of Allaah in ihram When they came near, each of us would lower her Jilbab from her head over her face, and when they passed by we would uncover our faces. Sunnan Abu Dawud 1:1833

From knowing what the terms mean, Muslim women choose how cover.  The majority of women choose to cover via a Hijab and Jilbab, as they believe the Niqab and Burqa were intended for the Prophet’s wives, and not all Muslim women. However, there are some Muslim women who believe it is a requirement to wear the Niqab or Burqa.