Hijab is the modern word for the practice of dressing modestly, which all practicing Muslims past the age of puberty are instructed to do in their holy book, the Qur'an. No precise dress code for men or women is set out in the Qur'an (the most specific part being 33:59 mentioning that believers "draw their cloaks close round them (when they go abroad)"), and various Islamic scholars have interpreted the meaning of hijab in different ways. The most basic requirements are that when in the presence of someone other than a close family member, a woman should cover her bosom, and walk and dress in a way which does not draw attention to her body, and that a man should be covered from at least the navel to his knees, and similarly not wear figure-hugging clothes that draw attention to his body. The way in which Muslims interpret this, if they choose to dress in accordance with hijab, varies greatly from individual to individual, and country to country.
The word "hijjab" is also frequently used specifically to mean a headscarf worn by a Muslim woman. In this case, it most often refers to a square scarf which is folded diagonally and worn over the head to cover the hair, ears and throat, but not the face. The word used in the Qu'ran for a headscarf is "khimar", which might be better to use when referring to headscarves in general, as many people argue that this use of "hijab" is incorrect, and it can certainly lead to confusion. See also: veil for a general description of headscarves and veils worn by both Muslim and non-Muslim women; and list of hats and headgear for a list of all kinds of veils.
Some liberal Muslims in the West choose to follow Hijab by dressing in a way that would be considered modest for the culture in which they find themselves - e.g. western business clothes.
The Taliban practice of forcing Afghan women to wear full burqas (a garment which covers the entire body, except for netting or a grille over the eyes for the women to see out of) was described as cruel and misogynistic, however very few Afghan women chose to take off their burqas after the Taliban fell (maybe some out of fear that even without the Taliban controlling their lives, Afghan society still frowned on their removing their burqas). Similarly the majority of Pakhtun women in the North Western Frontier Province of Pakistan continue to wear the burqa, even though there are no laws enforcing burqa-wearing in Pakistan.