Polygamy is defined in many dictionaries as: “Any person (male or female) may unconditionally marry unlimited number spouses at the same time."
This means that a male or female may marry an unlimited number of spouses at the same time. In other cultures and faiths, a male may marry an unlimited number of wives at the same time, for any reason, unrestricted by any conditions. Such practices are totally prohibited in Islam.
In Islam, a Muslim man is granted the right to marry more than one wife, accompanied by several clear conditions. These conditions are: financial, physical and emotional ability, equal treatment of the wives, that the women are not among those who are prohibited for him to marry permanently (such as aunts, foster daughters and others specified in the Quran) or temporarily (such as marrying two sisters at the same time); and that the number of wives is limited to four.
Hence, this is a legal provision that can be properly understood in the context of Islam's position on these issues. 
Polygamy can be of two types. One is polygene where a man marries more than one woman, and the other is polyandry, where a woman marries more than one man. In Islam, limited polygene is permitted and polyandry is completely prohibited. 
“… marry women of your choice, two or three or four; but if you fear that you shall not be able to deal justly with them, then only one.” (Quran 4:3)
The Quran limited the maximum number of wives to four. In the early days of Islam, those who had more than four wives at the time of embracing Islam were required to divorce the extra wives. Islam further reformed the institution of polygamy by requiring equal treatment to all wives. The Muslim is not permitted to differentiate between his wives in regards to sustenance and expenditures, time, and other obligations of husbands. Islam does not allow a man to marry another woman if he will not be fair in his treatment. Prophet Muhammad forbade discrimination between the wives or between their children.
You will never be able to do perfect justice between wives even if it is your ardent desire, so do not incline too much to one of them (by giving her more of your time and provision) so as to leave the other hanging (i.e. neither divorced nor married). And if you do justice, and do all that is right and fear Allah by keeping away from all that is wrong, then Allah Ever Oft-Forgiving, Most Merciful. Qur’an.Surah Nisa 4:129
Justice or fairness
..But if you fear that you shall not be able to deal justly (with them), then only one” [al-Nisa’ 4:3]
Narrated by Aisha Allah's Apostle (May Allah honour Him and Grant Him Peace) used to like sweets and also used to like honey, and whenever he finished the 'Asr prayer, he used to visit his wives and stay with them,Sahih Al Bukhari Vol 9: 102.
The ability to spend on one’s wives
In Islam, polygamy is allowed and practiced under certain restricted conditions. Qur'an is the only religious scripture in the world that says 'marry only one' Qur'an is the only religious book, on the face of this earth, that contains the phrase 'marry only one'. There is no other religious book that instructs men to have only one wife. Muslim men are allowed to practice polygene, that is, they can have more than one wife at the same time, up to a total of four.
“And if you fear that you cannot act equitably towards orphans, then marry such women as seem good to you, two and three and four; but if you fear that you will not do justice (between them), then (marry) only one or what your right hands possess; this is more proper, that you may not deviate from the right course.” Qur’an.Surah Nisa 4:3.
Polyandry is a practice wherein a woman has more than one husband at the same time. It is completely prohibited in Islam. Allah says in Qur’an “Also (forbidden are) women already married….” Qur’an.Surah Nisa 4:24. However this impediment is removed immediately if the marriage is dissolved either by the death of her former husband, or by divorce followed by completion of the period of 'Iddah (retreat or waiting period).
In Islam, a Muslim man is granted the right to marry more than one wife, accompanied by several clear conditions. These conditions are: financial, physical and emotional ability, equal treatment of the wives, that the women are not among those who are prohibited for him to marry permanently (such as aunts, foster daughters and others specified in the Qur’an.Surah Nisa 4:22-24) or temporarily (such as marrying two sisters at the same time). 
Narrated Abu Hurairah “The Prophet (saw) said: When a man has two wives and he is inclined to one of them, he will come on the Day of resurrection with a side hanging down [i.e. paralyzed]. Sunan Abu Dawood 2128. 
1 – Plural marriage helps to increase the numbers of the ummah (nation, Muslim community). It is known that the numbers can only be increased through marriage, and the number of offspring gained through plural marriage will be greater than that achieved through marriage to one wife.
2 – Statistics show that the number of women is greater than the number of men; if each man were to marry just one woman, this would mean that some women would be left without a husband, which would have a harmful effect on her and on society:
3 – Men are exposed to incidents that may end their lives, for they work in dangerous professions. They are the soldiers who fight in battle, and more men may die than women. This is one of the things that raise the percentage of husbandless women, and the only solution to this problem is plural marriage.
4 – There are some men who may have strong physical desires, for whom one wife is not enough. If the door is closed to such a man and he is told, you are not allowed more than one wife, this will cause great hardship to him, and his desire may find outlets in forbidden ways.
5 – Plural marriage does not exist only in the Islamic religion, rather it was known among the previous nations. Some of the Prophets were married to more than one woman. The Prophet of Allaah Sulaymaan (Solomon) had ninety wives. At the time of the Prophet (peace and blessings of Allaah be upon him), there were some men who became Muslims who had eight or five wives. The Prophet (peace and blessings of Allaah be upon him) told them to keep four wives and to divorce the rest.
6 – A wife may be barren, or she may not meet her husband’s needs, or he may be unable to have intercourse with her because she is sick. A husband may long to have children, which is a legitimate desire, and he may want to have a sex life within marriage, which is something permissible, and the only way is to marry another wife. It is only fair for the wife to agree to remain his wife and to allow him to marry another.
7 – A woman may be one of the man’s relatives and have no one to look after her, and she is unmarried or a widow whose husband has died, and the man may think that the best thing to do for her is to include her in his household as a wife along with his first wife, so that he will both keep her chaste and spend on her. This is better for her than leaving her alone and being content only to spend on her.
8 – There are other shar’i interests that call for plural marriages, such as strengthening the bonds between families, or strengthening the bonds between a leader and some of his people or group, and he may think that one of the ways of achieving this aim is to become related to them through marriage, even if that is through plural marriage. 
Islam Did Not Initiate Polygamy
Islam did not introduce polygamy. Among all Eastern nations of antiquity, polygamy was a recognized institution. Among the Hindus, polygamy prevailed from the earliest times. There was, as among the ancient Babylonians, Assyrians, and Persians, no restriction as to the number of wives a man might have. Although Greece and Rome were not polygamous societies, concubinage was a norm. Islam regulated polygamy by limiting the number of wives and bringing responsibility to its practice. In fact, according to David Murray, an anthropologist, historically polygamy is more common than monogamy.
The Catholic Encyclopedia: 
Cheryl Wetzstein, “Traditionalists Fear Same-Sex Unions Legitimize Polygamy,” The Washington Times 13 Dec. 2000. 
There are societies where women outnumber men. Besides these, wars take a heavier toll on men as compared to women. For unmarried women who cannot find husbands and widows who aspire to a respectable family life, polygyny is often an acceptable alternative.
Shaykh ‘Atiyyah Saqr, the ex-chairman of the Fatwa Center in Al-Azhar, says:
“Women are, by nature, not ready for fertilization during pregnancy and during menstruation, which is one fourth of every month until she reaches menopause. During the breastfeeding period, which can be as long as two years, a woman is usually disinterested in having sexual intercourse, except for a period of time every month when the ovum is ready for fertilization. Thus, it is fair and wise for polygene to be lawful, as long as the man can afford it and can be just.”
Therefore when Islam permits polygamy, it preserves a woman's dignity and humanity and cares for the social moral and economic well-being. The same principle applies when the number of women exceeds that of men in society. This would lead to moral depravity, which threatens the very essence of civilization.
The caller to Islam, Shaykh Muhammad Husayn ‘Eesa, says, “Many nations and religions before Islam would allow men to have a great number of wives. Some men were married to tens of women, and others to hundreds, without restrictions or conditions. When Islam came, it specified a number and stipulated a condition. It restricted the maximum number of wives to four. Narrated that Ibn 'Umar said:
“Ghailan bin Salamah became Muslim and he had ten wives. The Prophet said to him: 'Choose four of them.' ” Sahih Ibn Majah 1602 and Sahih in Musnad Ahmad Vol7:pg 95
Shaykh ‘Eesaa says that some men had five or eight wives when they embraced Islam, but the Prophet, forbade this and asked them to keep only four.