Mahram is an Arabic word which means a person, man or woman related to a particular individual by blood, marriage or breastfeeding. One he or she is not permitted to marry, such as the father or mother, brother or sister etc.
A mahram is a person one is never permitted to marry, because of a close blood relationship, breastfeeding or marriage.
- A close blood relationship: For a female, her father, grandfather, son, grandson, brother, both paternal and maternal uncles and nephews. Likewise for a male, his mother, daughter, granddaughter, sister, both paternal and maternal aunts and nieces.
- Breastfeeding: This includes anyone, male or female breastfed by the same mother or wet nurse. (and includes the brother or husband of the one who breastfed the person in question)
- Marriage: People who become your relations by marriage for example father-in-law, mother-in-law, stepfather, step-grandfather, and stepson.
When a woman is amongst her mahrams, the scholars of Islam agree that a woman does not have to observe strict rules of covering. However, a Muslim woman must always remember that she is known for her modesty and haya, therefore she must never make a wanton display of herself. 
The mahrams are those to whom marriage is permanently forbidden either because of blood ties or for a permissible reason, namely ties of marriage or ties created through breastfeeding. Allaah saysProhibited to you [for marriage] are your mothers, your daughters, your sisters, your father's sisters, your mother's sisters, your brother's daughters, your sister's daughters, your [milk] mothers who nursed you, your sisters through nursing, your wives' mothers, and your step-daughters under your guardianship [born] of your wives unto whom you have gone in. But if you have not gone in unto them, there is no sin upon you. And [also prohibited are] the wives of your sons who are from your [own] loins, and that you take [in marriage] two sisters simultaneously, except for what has already occurred. Indeed, Allah is ever Forgiving and Merciful. Quran Surah Nisa 4:23 
List of Mehram
- Their fathers: The woman’s father.
- Their husbands’ fathers: The husband’s father and grandfathers, up to all levels.
- Their sons: The woman’s sons down to all levels, and also the sons of daughters down to all levels.
- Their husbands’ sons: Male sons of the husband, including grandsons down to all degrees, whether they are sons of the husband’s sons or daughters.
- Their brothers: The woman’s brother
- Their brothers’ sons: The brother’s sons down to all degrees.
- Their sisters’ sons: The sister’s sons down to all degrees.
- Their women: Muslim, not polytheistic women, according to the preponderant opinion.
- That which their right hands possess: This may mean either: bondmaids or bondmen.
- Male attendants having no physical desire: They are men who are not at the same level as the women and have no interest in or desire for women; or the oblivious person who has no desire; an imbecile; and, an impotent man. The eunuch who can describe women is excluded.
- Children who are not yet aware of the private aspects of women: Because they are so young they do not understand anything about women or their ‘Awrah (parts of the body that must be covered). If a child is young and does not understand that, there is nothing wrong with him entering upon women, but if he is an adolescent or approaching adolescence, so that he knows and understands these things, and can make a distinction between a woman who is beautiful and one who is not, then he should not enter upon women. 
Shaykh Muhammad bin Saalih al-`Uthaymeenwas asked about the Awrah of the Women When it Comes to her Mahrams: He said- She is allowed to show to her Mahrams: her face, head, neck, hands, arms, feet, shanks (the part of the lower limb between the knee and the ankle), and she should cover everything else other than that. Hijab Marya wa zinatuqa, page 43 
See Also: MARRIAGE IN ISLAM; Awrah; WOMEN'S RIGHTS IN ISLAM